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Finding local maximum

  1. Jun 29, 2011 #1
    1. Show that the function F(x)=(sin(Nx)^2)/(sin(x)^2) has N-2 local maxima in the interval 0<x<pi



    2. Relevant equations



    3. I am stuck after i have calculated the derivate, (2Nsin(Nx)cos(Nx)sin(x)^2-2sin(x)cos(x)sin(Nx)^2)/sin(x)^4 = 0

    I am not sure how to simplify this equation, so far I have found 2N-1 local maximum and minimum, which is not correct. Please give me some hints.
     
  2. jcsd
  3. Jun 29, 2011 #2

    ehild

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    Try to plot the original function for small N-s. How many zeros has the original function in the interval (0, pi)?
    What are the minimal values of the function? What are limits at x=0 and at x=pi?

    ehild
     
    Last edited: Jun 29, 2011
  4. Jun 29, 2011 #3
    The original function has N-1 zeros on the interval (0,pi).
    The minimal values for the function is 0. And F->N^2 as x->0 and x->pi
    Wich means, if there are (N-1) zeros then there is (N-1)-1 = N-2 maximum.
    So I dont have to calculate the derivative.

    Thanks for the help ^^
     
  5. Jun 29, 2011 #4

    ehild

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    You have found out the solution earlier than me:smile:

    ehild
     
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