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Question
Find the intervals in which the following functions are strictly increasing or decreasing:
(x + 1)3 (x − 3)3
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Solution
f(x) (x + 1)3 (x - 3)3
f'(x) = 3(x + 1)2 (x - 3)3 + (x + 1)3 (3 (x - 3)2)
= 6(x + 1)2 (x - 3)2 (x - 1)
f'(x) = 6(x + 1)2 (x - 3)2 (x - 1)
if, f'(x) = 0
6(x + 1)2 (x - 3)2 (x - 1) = 0
x = -1, 1, 3
x = -1, x = 1, x = 3 splits the real line into intervals `(- infty, -1), (-1, 1), (1,3)` and `(3, infty)`.
The function f is decreasing on the interval `(-infty, -1)`.
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