Question 149
Determine all differentiable functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying simultaneously the conditions:
i) $f'(x)=0$ for every $x \in \mathbb{Z}$;
ii) for $x \in \mathbb{R}$, if $f'(x)=0$, then $f(x)=0$.
i) $f'(x)=0$ for every $x \in \mathbb{Z}$;
ii) for $x \in \mathbb{R}$, if $f'(x)=0$, then $f(x)=0$.