This came up in a recent discussion about l'Hopital's Rule. Suppose f(x) has a derivative at x=0, that is f'(0) exists. Is it necessarily true that f(x) is differentiable in some open interval containing x=0? Others--who know calculus better than I--say no, f(x) is not necessarily differentiable for x≠0. So my question is, what is an example function where that is the case? That is, f'(x) exists at x=0 f'(x) does not exist for x close to zero I'm unable to think of an example, but am quite curious about this.