Let $f(x) = \begin{cases} \text{sgn}(x) + x, & - \infty < x < 0 \\ -1 + \sin x, & 0 \le x \le \pi/2 \\ \cos x, & \pi/2 \le x < \infty \end{cases}$ …

Mathematics

Problem

Let

f(x) = \begin{cases} \text{sgn}(x) + x, & - \infty < x < 0 \\ -1 + \sin x, & 0 \le x \le \pi/2 \\ \cos x, & \pi/2 \le x < \infty \end{cases}

, then number of points where

f(x)

is not differentiable, is/are a. 0 b. 1 c. 2 d. 3