So, a certain discussion occured in class today...(adsbygoogle = window.adsbygoogle || []).push({});

If f is differentiable, is f ' continuous?

At first sight, there seems no reason to think so. However, we couldn't think any counterexample. It also seems logical that f' is continuous since otherwise f wouldn't be differentiable.

For example, suppose f(x) = ln x, for x > 0

Then f'(x) = 1/x. Yes, this is discontinuous, but it's not for the domain x > 0.

So, the question remains:

If f is differentiable, is f ' continuous?

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# If f is differentiable, is f ' continuous?

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