# Math Help - Extrema polar function

1. ## Extrema polar function

I need to find the point on r² = 4cos(2Ɵ) with the highest y-coordinate. I tried this using Lagrange multipliers, but I guess something went wrong during my calculation because when i sketch this polar graph, my point doesn't seem to fit. Can someone please check (and if possible, correct) this? Thanks!

2. ## Re: Extrema polar function

second page ...

$g(r,\theta) = 8\sin^2{\theta} - 4\color{red}\cos(2\theta)$

$g(r,\theta) = 8\sin^2{\theta} - 4\color{red}(1 - 2\sin^2{\theta})$

$g(r,\theta) = 16\sin^2{\theta} - 4$

$g(r,\theta) = 4(4\sin^2{\theta} - 1)$

3. ## Re: Extrema polar function

Thank you! Stupid mistake... I found that this point is (sqrt(3/2), 1/sqrt(2)) and (-sqrt(3/2), 1/sqrt(2)) !