CBSE Class 12-science Answered

Given f(x) = (x + 1)³(x - 1)³ 

f'(x)=3(x + 1)²(x - 1)³ + 3(x + 1)³(x - 1)² = 0 

f'(x) = 6x(x + 1)²(x - 1)² = 0

Solving, x = 0, x = -1 and x = 1

At these points, the slope is zero, so the function is neither increasing or decreasing

f'(x) = 6x(x + 1)²(x - 1)² >  0

Hence function is strictly increasing.

From -∞<x<-1 and from -1<x<0 the slope will negative and so the function will be strictly decreasing.
From 0<x<1 and from 1<x<∞ the slope will positive and so the function will be strictly increasing.