`f(x) = x^3 - 3x^2` Find the critical numbers of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the critical numbers of the function and for this reason, you must differentiate the function with respect to x, such that:

`f'(x) = (x^3 - 3x^2)'`

`f'(x) = 3x^2 - 6x`

You need to solve for x the equation f'(x) = 0:

`3x^2 - 6x = 0`

Factoring out 3x yields:

`3x(x - 2) = 0=> 3x = 0` or `x - 2 = 0`

`3x = 0=> x = 0`

`x - 2 = 0 => x = 2`

Hence, evaluating the critical values of the given function, yields x = 0 and x = 2.