list the critical number of the following function

Question

List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use.

G(x)=^3√3x^2-3x    The square root is over everything

 

a)=______

b)=______

c)=______

Answer 1

The critical numbers occur where this function's first derivative is equal to zero, or where it is undefined. Using the Power Rule and the Chain Rule, the derivative is:

 

f'(x) = (2x - 1)/(3x² - 3x)^2/3

 

This will equal zero when the numerator equals 0, which is at x = 1/2

 

It will be undefined when the denominator equals 0.

 

3x² - 3x = 3x(x - 1) = 0

 

This occurs at x = 0 and x = 1