How do you find the extrema of #f(x)=4 x^326 x^2+16x+1# on [0,3]?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the extrema of ( f(x) = 4x^3  26x^2 + 16x + 1 ) on the interval ([0,3]), follow these steps:
 Find the critical points by taking the derivative of ( f(x) ) and setting it equal to zero.
 Evaluate ( f(x) ) at the critical points and the endpoints of the interval ([0,3]).
 The maximum and minimum values of ( f(x) ) on the interval ([0,3]) will be the largest and smallest values obtained from step 2.
Let's proceed with the calculations:

( f'(x) = 12x^2  52x + 16 ). Set ( f'(x) = 0 ) and solve for ( x ) to find the critical points.
[ 12x^2  52x + 16 = 0 ]
Use the quadratic formula to solve for ( x ): [ x = \frac{{52 \pm \sqrt{52^2  4 \cdot 12 \cdot 16}}}{{2 \cdot 12}} ]
Simplify to find the critical points.

Evaluate ( f(x) ) at the critical points and endpoints.
Evaluate ( f(x) ) at ( x = 0 ), ( x = 3 ), and the critical points obtained from step 1.

Compare the values obtained in step 2 to determine the maximum and minimum values of ( f(x) ) on the interval ([0,3]).
This process will yield the extrema of the function ( f(x) ) on the interval ([0,3]).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 If #f(x)= x^44x^3+4x^21#, how do you find all values of #x# where the graph of #f# has a horizontal tangent line?
 Let f:Rise defined from R to R . find the solution of f(x) =f^1 (x)?
 How do use the first derivative test to determine the local extrema #f(x) = x³+3x²9x+15#?
 How do you find the local extrema for #f(x) = x  ln(x)# on [0.1,4]?
 Given #f(x) = 2(x+2)(x1)^2# on the open interval (3,3). How do you determine the x coordinate of the relative minimum of f (x) in the open interval (3,3)?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7