Question

Function $f\left(x\right)=$ max $(|\tan x|,|\cos x|)$ is

• A. not differentiable at $4$ point in $(-\pi ,\pi )$
• B. discontinuous at $2$ point in $(-\pi ,\pi )$
• C. not differentiable at only $2$ point in $(-\pi ,\pi )$
• D. none of these

Answer 1

The correct option is A not differentiable at $4$ point in $(-\pi ,\pi )$

Given ,$f\left(x\right)$= max $(|\tan x|,|\cos x|)$
If we graph $f\left(x\right)$, we get a symmetrical continuous function about $(0,0)$ with $2$ non differentiable points in $[0,\pi )$
Thus, there are total $4$ points of non diffrentiability in $(\pi ,\pi )$, since the function is symmetric about $(0,0)$
So the correct option is (A).