Question

Let $f:\left[- 1 , 1\right] \rightarrow R$ be a function defined by $f\left(x\right)=min \left\{\left|x\right| , \sqrt{1 - x^{2}}\right\}.$ If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly

• A. one element
• B. two elements
• C. five elements
• D. three elements

Answer 1

Answer: (C)

Graph of given function $f\left(x\right)=min \left\{\left|x\right| , \sqrt{1 - x^{2}}\right\},$ is as shown

Clearly, $f\left(x\right)$ is not differentiable at $5$ points in $\left[- 1 , 1\right]$ .