# Does derivative have to be piecewise continous

1. Jul 6, 2009

### causalset

I know the derivative does not have to be continous, due to couter-example $f(x)=x^2 \sin (1/x)$. But does derivative still have to be PIECEWISE continuous? If not, is there some weaker statement that is still true?

2. Jul 6, 2009

### g_edgar

the derivative has the Darboux property... http://planetmath.org/encyclopedia/DarbouxsTheorem.html" [Broken]

Last edited by a moderator: May 4, 2017
3. Jul 6, 2009

### causalset

Are you saying that derivative does NOT have to be piecewise continuous, or are you saying you simply don't know one way or the other?

Last edited by a moderator: May 4, 2017