Question:
Let $S$ be the set of all points in $(-\pi, \pi)$ at which the function $f(x)=\min \{\sin x, \cos x\}$ is not differentiable. Then $S$ is a subset of which of the following?
Correct Option: , 2
Solution:
$f(x)=\min \{\sin x, \cos x\}$
$\because f(x)$ is not differentiable at $x=-\frac{3 \pi}{4}, \frac{\pi}{4}$
$\therefore \quad S=\left\{-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$
$\Rightarrow \quad S \subseteq\left\{-\frac{3 \pi}{4}, \frac{-\pi}{4}, \frac{3 \pi}{4}, \frac{\pi}{4}\right\}$