Question

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

Answer 1

The function $f\left(x\right)=\left|x-0\right|+\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+\left|x-4\right|$ is continuous everywhere

but not differentiable at x = 0,1,2,3 and 4