This came up in a recent discussion about l'Hopital's Rule.(adsbygoogle = window.adsbygoogle || []).push({});

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=0I'm unable to think of an example, but am quite curious about this.

f'(x) does not exist for xclose tozero

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# F(x) differentiable at / near x=0?

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