Question

How do you find the local maximum and minimum values of `f ' (x) = (x^2 -9)`?

Answer 1

at local max or min `f'(x)` is zero.

=> `x^2 -9 = 0`
=> `x^2 = 9`
=> `x = +-sqrt9 = +- 3`
so at `x =+- 3` , the function is either max or min (locally).