Possible Duplicate:
Proof of a simple property of real, constant functions.
Suppose $|f(x)-f(y)|\leq (x-y)^2$ for all $x,y\in\mathbb{R}$. Show f is differentiable.
This follows intuitively, the derivative $2(x-y)$ is defined on $\mathbb{R}$. How do I show this formally?