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Convex function

  1. May 24, 2004 #1
    Hello,

    how can I proof this:
    given: a convex function on an open interval I,which is a subset of R.
    I have to show that the function can be differentiated on the whole interval.
    I already proved the following for a<b<c, a,b,c in I:
    f(b)-f(a))/(b-a)<(f(c)-f(a))/(c-a)<(f(c)-f(b))/(c-b).

    Thanks for help!
    Jonas
     
  2. jcsd
  3. May 24, 2004 #2

    HallsofIvy

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    Isn't f(x)= |x| convex on I= (-1,1)?
     
  4. May 24, 2004 #3
    Ah, sorry,
    actually one has to show that the function is differentiable from the left and from the right(but these derivatives don´t have to be equal, as your example shows clearly).
    Jonas
     
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