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How to use Rolle's Theorem to prove exactly ONE REAL ROOT

  1. Nov 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that the equation 2x-1-sin(x) = 0 has exactly one real root.

    2. Relevant equations

    3. The attempt at a solution
    I first used the Intermediate Value Theorem to prove that there exists at least one c such that f '(c)=0. The next step requires Rolle's Theorem to prove that there is EXACTLY ONE REAL ROOT, but I have no idea how to proceed at this point.
  2. jcsd
  3. Nov 7, 2008 #2


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    I think you mean that you used the IVT to show there is a least one value of c such that f(c)=0. Not f'(c). f'(x) is never zero. Can you show that? If so what does Rolles theorem tell you if f(x)=0 had multiple roots.
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