Let $f\left(x\right)=\min \left\{\sqrt{4-x^2},\sqrt{1+x^2}\right\} \forall x\in \left[-2,2\right]$, then the number of points where $f\left(x\right)$ is non-differentiable is

• A

  $1$
• B

  $0$
• Correct answer
  C

  $4$
• D

  $2$

Solution

Clearly, from the graph we can see that $f\left(x\right)$ is non-differentiable at $4$ points

Hence, the correct answer is option: 'C'.