Question

An example of function which is continuous everywwhere but not differentiable at exactly at two points is

• A. $f\left(x\right)=|x|+|x-1|$
• B. $f\left(x\right)=|x+1|+|x|-|x-3|$
• C. $f\left(x\right)=|x+1|-|x-3|+|x-7|$
• D. None

Answer 1

The correct option is A $f\left(x\right)=|x|+|x-1|$

Consider the function $f\left(x\right)=|x|+|x-1|$
$f$ is continuous every where but it is not differentiable at $x=0$ and $x=1$.