# Finding local maximum

1. Jun 29, 2011

### zardiac

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. Jun 29, 2011

### ehild

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
3. Jun 29, 2011

### zardiac

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 ^^

4. Jun 29, 2011

### ehild

You have found out the solution earlier than me

ehild