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Non-Injective functions

  1. Nov 10, 2007 #1
    If an interval is differentiable, but not injective, will there be a point where the derivative f'(x)=0 on that interval?

    I'm not really sure how to approach this question. Help plz?
     
    Last edited: Nov 10, 2007
  2. jcsd
  3. Nov 10, 2007 #2

    HallsofIvy

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    Use the mean value theorem. f f(x) is not injective, then there must exist x1 and x2 such that f(x1)= f(x2). Apply the mean value theorem to the interval [x1, x2].
     
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