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Differentiation problem

  1. Jan 1, 2009 #1
    Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f[tex]\acute{}[/tex](1-c) = -f[tex]\acute{}[/tex](c).

    thanks for any suggestions.
  2. jcsd
  3. Jan 1, 2009 #2
    Just from the givens it made me think of MVT...
  4. Jan 1, 2009 #3
    That was my first impression but it seems to be a little trickier than that.
  5. Jan 1, 2009 #4


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    It's a little more complicated, but not much. Define g(x)=f(x)+f(1-x). g(0)=g(1), right?
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