1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

    Re: Mean value theroem??

    Have you noticed that the function is even? :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook