Critical Numbers for f(x)=2sin(2x)/x on [-pi,pi]

  • Thread starter Thread starter cdhotfire
  • Start date Start date
  • Tags Tags
    Numbers
cdhotfire
Messages
193
Reaction score
0
Well, I got this equation f(x)=\frac{2\sin{2x}}{x} [-\pi,\pi]
So I took the 1st derivative, f'(x)=\frac{2(2x\cos{2x} - \sin{2x})}{x^2}
Then I set that equal to 0, and got 0=2x\cos{2x} - \sin{2x}
But I do not see how to get the critical numbers, I also tried to do double angle, but that just resulted in more pain.:mad:
Any help, would be appreciated.:smile:
 
Physics news on Phys.org
Please.:rolleyes:
 
Haven't I seen this somewhere before? :)
 
Tide said:
Haven't I seen this somewhere before? :)

ya, i know, i though no one visited the mathematics section, because i was only able to join it by using the search tool. Also, i put a note for someone to delete my post in the other section.:smile:

btw, i posted back on you reply.:-p
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top