Solve this following
Question:

Let $f(x)= \begin{cases}\max \left\{|x|, x^{2}\right\}, & |x| \leq 2 \\ 8-2|x|, & 2<x \mid \leq 4\end{cases}$

Let $S$ be the set of points in the interval $(-4,4)$ at which $\mathrm{f}$ is not differentiable. Then $S$ :

1. is an empty set

2. equals $\{-2,-1,1,2\}$

3. equals $\{-2,-1,0,1,2\}$

4. equals $\{-2,2\}$

Correct Option: , 3

Solution:

$f(x)= \begin{cases}8+2 x, & -4 \leq x<-2 \\ x^{2}, & -2 \leq x \leq-1 \\ |x|, & -1<x<1 \\ x^{2}, & 1 \leq x \leq 2 \\ 8-2 x, & 2<x \leq 4\end{cases}$

$f(x)$ is not differentiable at $x=\{-2,-1,0,1,2\}$

$\Rightarrow S=\{-2,-1,0,1,2\}$