If $f$ is Lipschitz of order 1 at $x$, is it differentiable at $x$?
A function $f$ is Lipschitz of order $\beta$ at $x$ if there is a constant D such that
$$|f(x)-f(y)|\le D \,|x-y|^\beta$$
for all $y$ in the interval containing $x$.
If yes, can anyone motivate a proof for me?