i got a problem with this exercise:

Be $f:\;\mathbb{R\rightarrow\mathbb{R}}$ a function such that 

$|f(x)-f(y)|\leq(x-y)^{2}$, $\forall x,y\in\mathbb{R}$

Prove $f$ is constant.

Well... i was thinking about make this exercise for reduction to absurdity. I suppose exist $c\in(x,y)$ such that $f'(c)\neq 0$ if that happen then $f(x)\neq f(y)$ for $x,y \in \mathbb R$. Some ideas? please help :l i'm stuck in this exercise.