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Mean Value Theorem Problem

  1. Oct 21, 2008 #1
    Use the mean value theorem to show that (abs. value of tan^-1 a) < (abs. value a) for all a not equal to 0. And use this inequality to find all solutions of the equation tan^-1 x = x.

    I have no idea how to do this.


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 21, 2008 #2

    Mark44

    Staff: Mentor

    Start with what the mean value theorem says, and go from there.
     
  4. Oct 21, 2008 #3
    Well MVT is, if f is cont. on [a,b] and differentiable on (a,b). Then there exists a number c E (a,b) such that: f '(c) = f(b) - f(a)/b-a

    But I don't get how to apply that here.
     
  5. Oct 21, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, taking f(x)= tan-1[sup(x) would be a start. What is the derivative of tan-1(x)?
     
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