CBSE Class 12-science Answered
Find the intervals in which the function f(x)=(x+1)^3(x-1)^3 is strictly increasing or decreasing.
Asked by lekhakarthikeyan | 13 Sep, 2018, 02:09: AM
Expert Answer
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.
Answered by Sneha shidid | 13 Sep, 2018, 02:50: PM
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