Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

    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?

    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


    User Avatar
    Homework Helper

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

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook