Intermediate Value Theorem and Rolle's Theorem to show root

  1. 1. The problem statement, all variables and given/known data
    Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root.


    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure what the question is asking for. the theorems I believe are to prove the existence of a point between a closed interval, but I have no interval, and what does it mean by "one root"
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. LCKurtz

    LCKurtz 8,392
    Homework Helper
    Gold Member

    Hint: Check f(0) and f(pi). And "one root" means the graph touches the x axis only once. And if you find one root, what can you conclude from Rolle's theorem if you have another root?
     
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