`f(x) = (x+2)^2(x- 1)` Find the critical numbers, open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.
This function is defined everywhere, its critical numbers are where f'(x)=0.
f'(x)=2*(x+2)*(x-1) + (x+2)^2 =
(x+2)*(2x-2+x+2) = (x+2)*(3x).
This is =0 at x=-2 and x=0. Also f'(x) is negative for x in (-2, 0) and positive in `(-oo, -2) uuu (0, +oo).` The function f is decreases and increases correspondently. Therefore x=-2 is the local maximum and x=0 is a local minimum.