Question

Let $f\left(x\right)=min\{1-\left|x\right|,x^2-1\}$, then

• A. $f\left(x\right)$ is increasing function
• B. $f\left(x\right)$ is always differentiable
• C. $f\left(x\right)$ is decreasing at $x=1$
• D. $f\left(x\right)$ is non-differentiable at exactly $2$ points

Answer 1

The correct option is D $f\left(x\right)$ is non-differentiable at exactly $2$ points

The dark shaded part of curves is the graph of $f\left(x\right)$

clearly , $f\left(x\right)$ is not differentiable at

$x=1$ and $x=-1$