# 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
7 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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