If a function is differentiable in [a,b] then its derivative is continious almost everywhere

Asked Dec 01 '17 at 20:16

Active Dec 01 '17 at 20:39

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Is it true that for every differentiable function $f:[a,b]\rightarrow\mathbb{R}$ its derivative $f'$ is continious in $[a,b]$ and it can be discontinious in isolated points? If not, then can you find a counterexample?

PS: If there is a problem in the translation let me now.

edited Dec 01 '17 at 20:39

asked Dec 01 '17 at 20:16

Lerigorilla

3

This looks related: https://math.stackexchange.com/questions/112067/how-discontinuous-can-a-derivative-be. From the answer: "D (the discontinuity set) can have positive measure." – Martin R Dec 01 '17 at 20:21
Not every function even has a derivative; do you mean for every differentiable function? – Sort of Damocles Dec 01 '17 at 20:22
Yes sorry I mean differentiable. – Lerigorilla Dec 01 '17 at 20:39
Your title makes sense, but your first sentence below it makes no sense. – zhw. Dec 01 '17 at 20:56
If it's Lipschitz, you can use Radamacher's theorem to get that the function is differentiable a.e. – parsiad Dec 02 '17 at 04:14

If a function is differentiable in [a,b] then its derivative is continious almost everywhere

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