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