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

Consider the function 
 $f\left(x\right)=\max \{-\left|x\right|,-\sqrt{1-x^2}\}$
Now, the graph of the function 
   
From the graph, it is clear that $f\left(x\right)$  is not differentiable at 
$x=0,-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ ; Then,  $K=\{-\frac{1}{\sqrt{2}},0,\frac{1}{\sqrt{2}}\}$
Hence,  $K$ has exactly three elements.