Let Then the number of points where is not differentiable is

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)=\begin{cases}\operatorname{sgn}(x)+x, & -\infty<x<-1,\\-1+\sin x, & -1\le x\le\frac{\pi}{2},\\\cos x, & \frac{\pi}{2}\le x<\infty.\end{cases}

Then the number of points where

f(x)

is not differentiable is (1) 0 (2) 1 (3) 2 (4) 3