RO-NMO 2015 Problem 111

Find all differentiable functions $f:\mathbb{R}\longrightarrow\mathbb{R}$ that verify the conditions: $\text{(i)} \forall x\in\mathbb{Z} f'(x) =0$ $\text{(ii)} \forall x\in\mathbb{R} f'(x)=0\implies f(x)=0$