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Find the intervals in which the function f(x)=(x+1)^3(x-1)^3 is strictly increasing or decreasing.

Asked by lekhakarthikeyan 13th September 2018, 2:09 AM
Answer Verified by Expert
Answer:

Given f(x) = (x + 1)3(x - 1)3 

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

Verified by Expert 13th September 2018, 2:50 PM
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