Find the local maxima or local minima of f(x) = (x -1)(x+2)^2

Question

Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:

f(x) = (x -1)(x+2)²

Answer 1

local max. value is 0 at x = −2 and local min. value is −4 at x = 0

f’(x) = (x -1)2(x+2)+(x+2)² = 0

x = 0,-2

f’’(0)>0, 0 is the point of local min.

f’’(-2)<0, -2 is the point of local max.

f(0) = -4

f(-2) = 0