What are the critical points of # f(x) = (x - 3sinx)^4 -xcosx#?

Question

Elijah Abram · Accepted Answer

Critical Points are where the derivative is equal to 0.  But we need to find the derivative. In order to do so, I'll split up #f(x)# into two parts -PART 1 =  #(x-3sin(x))^4# and PART 2 = #xcos(x)# and I will combine them using the Sum Rule later.  PART 1: Let's apply the Chain Rule.  #d/dx(x-3sin(x))^4=4*(x-3sin(x))^3*(1-3cos(x))#
#=4(x-3sin(x))^3(1-3cos(x))# PART 2: Let's apply the Product Rule. #d/dx xcos(x)=1*cos(x)+x*-sin(x)#
#=cos(x)-xsin(x)# #therefore f'(x)# is: #=4(x-3sin(x))^3(1-3cos(x))-(cos(x)-xsin(x))#
#=xsin(x)-cos(x)+4(x-3sin(x))^3(1-3cos(x))# (Rearranging and expanding #-(cos(x)-xsin(x))#) Now all you have to do is set that equal to 0: #xsin(x)-cos(x)+4(x-3sin(x))^3(1-3cos(x))=0# ...

Aurora Alvarado · Answer

undefined To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we needTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first needTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivativeTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solveTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve forTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equalsTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zeroTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero orTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or isTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefinedTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ whenTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined.To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when theTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. ThenTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivativeTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then,To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equalsTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, weTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zeroTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve forTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ fTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

TheTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative ofTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) =To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ fTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ withTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respectTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect toTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sinTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $,To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted asTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ fTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cosTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $,To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x))To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, isTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is givenTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ fTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) =To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sinTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x -To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

CriticalTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical pointsTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sinTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occurTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdotTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 -To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cosTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sinTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x))To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cosTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x)To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) -To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sinTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cosTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x)To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x))To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) \To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

NowTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cosTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now,To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, weTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) -To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x)To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) =To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal toTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

SolveTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve thisTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equationTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation forTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

$$ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ xTo find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x \To find the critical points of \( f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ toTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x -To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to findTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find theTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find the criticalTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\sinTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find the critical pointsTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\sin(xTo find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find the critical points.To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\sin(x))^To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find the critical points.To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\sin(x))^3To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we first need to find its derivative and then solve for $ x $ when the derivative equals zero.

$ f'(x) = 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) $

Critical points occur where $ f'(x) = 0 $.

$ 4(x - 3\sin(x))^3(1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $

Solve this equation for $ x $ to find the critical points.To find the critical points of $ f(x) = (x - 3\sin(x))^4 - x\cos(x) $, we need to find where the derivative of $ f(x) $ equals zero or is undefined. Then, we solve for $ x $.

The derivative of $ f(x) $ with respect to $ x $, denoted as $ f'(x) $, is given by:

\[ f'(x) = 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) $$

Now, we set $ f'(x) $ equal to zero and solve for $ x $:

$$ 4(x - 3\sin(x))^3 \cdot (1 - 3\cos(x)) - \cos(x) - x\sin(x) = 0 $$

This equation may not have a closed-form solution, but numerical methods or graphical analysis can be used to approximate the critical points. These points are where the derivative is zero or undefined.