Question 23
Find all differentiable functions $f : \mathbb{R} \to \mathbb{R}$ for which:
i) $f'(x) = 0$, for all $x \in \mathbb{Z}$;
ii) if $f'(x) = 0$ for some $x \in \mathbb{R}$, then $f(x) = 0$.
i) $f'(x) = 0$, for all $x \in \mathbb{Z}$;
ii) if $f'(x) = 0$ for some $x \in \mathbb{R}$, then $f(x) = 0$.