The prompt is to find the maximum value of the function $f(x) = 10 - 5x^2 -9y^2$ over the region $4x^2+y^2 \leq 4$.
This is what I tried doing, The method of Lagrange multipliers says that extrema of $f(x, y)$ subject to the constraint are found among the solutions of $\nabla(x, y) = \lambda\nabla g(x, y)$, where
This will only give us 2 values of $\lambda$ ,$\frac{5}{4}$ and $-9$ but x and y are still 0
I'm lost now what to do with $\lambda$ since my points are (0, 0) how to proceed with this problem?