Consider the function $f\left(x\right)=\min \left\{\left|x^2-4\right|,\mathrm{}\left|x^2-1\right|\right\}$, then the number of points where $f\left(x\right)$ is non-differentiable is/are

• A

  $0$
• B

  $7$
• Correct answer
  C

  $6$
• D

  $4$

Solution

Using the graph of $y=\left|x^2-4\right|,\mathrm{}y=\left|x^2-1\right|$

Clearly, from the graph we can see $f\left(x\right)$ is non-differentiable at $6$ points.

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