Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$ Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$.


This question is just after the definition of differentiation and the theorem that if $f$ is finitely derivable at $c$, then $f$ is also continuous at $c$. Please help, my textbook does not have the answer.
$$\ \ \ \ \mathsf{W}\ \ \ \ $$
How about $f(x) = \max(\sin(n\pi x),0)$ or perhaps $g(x) = |\sin(n\pi x)|$?