Given, as f(x) = (x – 1) (x + 2)2
On differentiating with respect to x, we get,
f‘(x) = (x + 2)2 + 2(x – 1)(x + 2)
= (x + 2) (x + 2 + 2x – 2)
= (x + 2) (3x)
For all the maxima and minima,
f’(x) = 0
= (x + 2) (3x) = 0
On solving the above equation we get
= x =0, – 2
At x = – 2 f’(x) changes from negative to positive
Since, x = – 2 is a point of Maxima
At x =0 f‘(x) changes from negative to positive
Since, x = 0 is point of Minima.
Thus, local min value = f (0) = – 4
Local max value = f (– 2) = 0.