Question

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

Answer 1

$f\left(x\right)=\left|x\right|+\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|$
The above function is continuous everywhere but not differentiable at x = 0, 1, 2, 3 and 4