Question

Let $f\left(x\right)=max(\left\{x\right\},sgnx,\{-x\}),\{.\}$denote fraction part function $\forall xϵ[-5,5]$,then number of points in interval$[-5,5]$where $f\left(x\right)$ is not differentiable is

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is D $11$

The given function will graphically transformed as above.

for $x\in (0,5],f\left(x\right)=sgn\left(x\right)=1$

for $x=\left\{x\right\}=\{-x\}$ at $x=-5,-4,-3,-2,-1,0$

In the graph , the points at which $f\left(x\right)$ is not differentiable is marked in red.