Could somebody please shed some light on this problem?
Let $x,y \in \mathbb R$, we wish to maximize $f(x,y)=\frac{x^2-y^2}{(x^2+y^2)^2}$ by finding suitable values of $x,y$.
Setting $\partial f\over \partial x$ and $\partial f \over \partial y$ as $0$ gives
$x(x^2-3y^2)=0=y(y^2-3x^2)$ but these give $x=y=0$ which is not acceptable! Any ideas?
Thank you.