Prove that the function f given by f (x) = log |cos x| is strictly decreasing onand strictly increasing on.

Question

Prove that the function f given by f (x) = log |cos x| is strictly decreasing on and strictly increasing on .

Philoid · Accepted Answer

It is given that f (x) = log |cos x|

In interval, f’(x) = -tanx < 0

Therefore, f is strictly decreasing on.

In interval, f’(x) = -tanx > 0

Therefore, f is strictly increasing in.