What are the critical values of #f(x)=(3x)^2x#?
Find the first derivative by using distribution :
By signing up, you agree to our Terms of Service and Privacy Policy
To find the critical values of ( f(x) = (3  x)^2  x ), we need to first find the derivative of the function and then set it equal to zero to solve for critical points. After finding the critical points, we can determine whether they correspond to maximum, minimum, or inflection points.

Calculate the derivative of ( f(x) ) with respect to ( x ): [ f'(x) = 2(3  x)(1)  1 ]

Simplify the derivative: [ f'(x) = 2(3  x)  1 ] [ f'(x) = 6 + 2x  1 ] [ f'(x) = 7 + 2x ]

Set the derivative equal to zero and solve for ( x ) to find critical points: [ 7 + 2x = 0 ] [ 2x = 7 ] [ x = \frac{7}{2} ]

Check for the nature of the critical point by examining the sign of the derivative around ( x = \frac{7}{2} ):
 When ( x < \frac{7}{2} ), ( f'(x) < 0 ), indicating the function is decreasing.
 When ( x > \frac{7}{2} ), ( f'(x) > 0 ), indicating the function is increasing.
Thus, the critical value of ( f(x) ) is ( x = \frac{7}{2} ).
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.
 What are the local extrema of #f(x)= lnx/e^x#?
 How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = x^3 + x^2# on the interval [0,1]?
 How to find the maximum and minimum when given derivative?
 What is the local maximum and or miminum of the function #f(x)=2x^2+2x^24x#?
 How do use the first derivative test to determine the local extrema #f(x) = x^3  x^2  x + 3#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7