Is a Lipschitz function differentiable?
I have been wondering whether or not this property applies to all functions.
I do not need a formal proof, just the concept behind it.
Let $f: [a,b] \to [c,d]$ be a continuous function (What is more - it is uniformly continuous!) And let's assusme that it's also Lipschitz continuous on this interval.
Does this set of assumptions imply that $f$ is differentiable on $(a,b)$?