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Homework Help: Mean value theroem?

  1. Mar 10, 2012 #1
    Mean value theroem??

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

    Show that [tex] x^2 = xsinx + cosx [/tex] is true only for two values of [tex] x \in {R} [/tex]

    2. Relevant equations

    Intermediate value theorem
    Mean value theorem (?)

    3. The attempt at a solution

    I already know how to prove that there is al least one [tex] x \in [1,1.5] [/tex] and another [tex] x \in [-1.5,-1] [/tex] where the equation holds. The thing is that I'm not completely sure how to pove that they are unique, I have a geometric argument buy i feel it can be done using the mean value theorem.

    Just for you to know, what i did to find out where the x's are, i took [tex] f(x) = x^2-xsinx-cosx [/tex] and gave values to the function it turns out that [tex] f(1) < 0 [/tex] and [tex] f(1.5) > 0 [/tex] so there must be at leat one [tex] x \in [1,1.5] [/tex] where [tex] f(x) = 0 [/tex] But that's it, I ran out of ideas although i feel I'm really close.

    Any ideas or advices will be appreiciated
     
  2. jcsd
  3. Mar 11, 2012 #2

    Mentallic

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    Homework Helper

    Re: Mean value theroem??

    Have you noticed that the function is even? :smile:
     
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