Question

Write a function which is differentiable at infinite many points as well as non-differentiable at infinite many points.

Answer 1

a function which is differentiable at infinite many points:

$f(x)=e^x$ is differentiable at $x\in (\infin,\infin)$

a function which is non-differentiable at infinite many points:

$f(x)=tanx$ has not derivative at $x=\pi /2+\pi n,\ n\isin Z$