I've tried using Lagrange multipliers, but my problem is the equation system: $$\left\lbrace \begin{array}{ll} 8x=\alpha(8x) \\ 4y=\alpha(2y) \\ 4x^2+y^2-4=0 \end{array} \right.$$
I do not know what to do in this step
2026-03-30 05:26:53.1774848413
How to find the ends with restrictions function $f(x,y)=4x^2+2y^2+10$, subject to $4x^2+y^2=4$
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Hint (Without Lagrange)
Under the restriction your function is
$$ f(x,y) = y^2 + 14 $$ Since $0\leq y^2 \leq 4$, you can find the end points pretty fast.