CBSE Class 12-science Answered
Find the intervals in which f (x) = (x + 1)3 (x - 3)3 is increasing or decreasing.
Asked by Topperlearning User | 06 Aug, 2014, 09:54: AM
Expert Answer
We have,
f (x) = (x + 1)3 (x - 3)3
=> f ' (x) = 3(x + 1)2
(x + 1)(x - 3)3 + (x + 1)33(x - 3)2.
(x - 3)
=> f ' (x) = 3(x + 1)2 (x - 3)3 + 3(x + 1)3 (x - 3)2
=> f ' (x) = 3(x + 1)2 (x - 3)2 (x + 1 + x - 3)
=> f ' (x) = 3(x + 1)2 (x - 3)2 (x + 1 + x - 3)
=> f ' (x) = 6(x + 1)2 (x - 3)2 (x - 1)
For f (x) to be increasing, we must have
f ' (x) > 0
=> 6(x + 1)2 (x - 3)2 (x - 1) > 0 x - 1 > 0 [
6(x + 1)2 (x - 3)2 > 0]
=> x > 1 & x belongs to (1, ¥)
So, f (x) is increasing on (1, ¥)
For f (x) to be decreasing, we must have
f ' (x) < 0
=> 6(x + 1)2 (x - 3)2 (x - 1) < 0
=> x - 1 < 0 [ 6(x + 1)2 (x - 3)2 > 0]
=> x < 1 & x (-¥, 1)
So, f (x) is decreasing on 
Answered by | 06 Aug, 2014, 11:54: AM
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