Find the maximum and minimum values of $f(x,y)=y^2-4x^2$ about the constraint: $x^2+2y^2=4$
When I do the usual Lagrange Multiplier method, the equations come out rather strange: $\nabla f=\lambda \nabla g$ where $g$ is the constraint.
$-8x=\lambda2x$ and $2y=\lambda4y$
which yields different values for $\lambda$. How do I go about solving for the optimization points when this happens?
Any hints would be appreciated.