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Question involving differentiation

  1. Dec 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that if F is a twice differentiable function with F(0) = 0 and F(1) = 1 and F'(0) = F'(1) = 0, then |F''(x)| >= 4 for x in (0,1).

    Hint: Prove that either F"(x) >= 4 for some x in (0,1/2) or else F"(x) <= -4 for some x in (1/2,1)

    Then, show that we actually have |F"(x)| > 4.
    2. Relevant equations
    I suppose we'll be using the mean value theorem..

    3. The attempt at a solution

    No tangible idea as to where to start..

  2. jcsd
  3. Dec 23, 2009 #2


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    Homework Helper

    have you had a look at rolle's theorem?
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