Originally Posted by

**tubetess123** I need to find the global maximum and minimum of the function

(3x^2+2xy+y^2)/(x^2-2xy+3y^2).

I did the partial derivatives, set them equal to zero, took the numerator since the function will only equal zero when the numerator is zero, and got the following:

y(-x^2+2xy+y^2) = 0 and 0 = x(x^2-2xy-y^2)

I know that (x,y) can't equal (0,0) because the function is undefined there, so I need to find other (x,y) so that -x^2+2xy+y^2 = 0 and x^2-2xy-y^2 = 0. I recognized that those are both quadratic equations, so I used the quadratic formula to find y in terms of x and got

y = (-1(+/-)2^.5)x

I don't know what to do from there. How do I find the critical points now that I have that equation for y?

Thanks!