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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
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