Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does derivative have to be piecewise continous

  1. Jul 6, 2009 #1
    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. jcsd
  3. Jul 6, 2009 #2
    the derivative has the Darboux property... http://planetmath.org/encyclopedia/DarbouxsTheorem.html" [Broken]
    Last edited by a moderator: May 4, 2017
  4. Jul 6, 2009 #3
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook