Given $|f(x) - f(y)| \leq M|x-y|^2$ , prove that f is constant.

Let f be differentiable on R and suppose that there exists M > 0 such that, for any x, y $\in$ R, $|f(x) - f(y)| \leq M|x-y|^2$. Prove that f is a constant function.


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