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Find the intervals in which f(x) = logcosx is strictly decreasing and strictly increasing.

Find the intervals in which f(x) = logcosx is strictly decreasing and strictly increasing.

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(x) = \log (cos(x))
f^{'}(x) = \frac{-sinx}{cosx} = -tanx
f(x) is increasing in the interval where
-tanx> 0
tanx< 0
(n-\frac{1}{2})\pi < x< n\pi
f(x) is decreasing in the interval where
tanx>0
n\pi< x< (n+\frac{1}{2})\pi
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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