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