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

at local max or min $f ' \left(x\right)$ is zero.
=> ${x}^{2} - 9 = 0$
=> ${x}^{2} = 9$
=> $x = \pm \sqrt{9} = \pm 3$
so at $x = \pm 3$ , the function is either max or min (locally).