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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# If f is differentiable, is f ' continuous?

**Physics Forums | Science Articles, Homework Help, Discussion**