Question

If $f\left(x\right)=\left|\begin{array}{c}|x{|}^2-2|x|-3\end{array}\right|,$ then $f\left(x\right)$ is not differentiable at $x$ equal to

• A. $-1,0,1$
• B. $1,2$
• C. $-3,-1,0,1,3$
• D. $-3,0,3$

Answer 1

The correct option is D $-3,0,3$

$f\left(x\right)=\left|\begin{array}{c}|x{|}^2-2|x|-3\end{array}\right|$
The graph of the function $f\left(x\right)$ is obtained as:



From graph of $||x{|}^2-2|x|-3|$ it is evident that at $x=-3,0,3$ it has sharp edges.
$\therefore$ At $x=0,3,-3,f\left(x\right)$ is not differentiable.