If $f(x,y) = x ^2 + xy + y^2 - 4 \ln x - 10 \ln y,$ and I found the critical points to be {(1,2), (-1,-2),$(4/\sqrt{3}, -5/\sqrt{3})$, $(-4/\sqrt{3}, 5/\sqrt{3}) $} .... should I exclude the points containing negative values of $x$ & $y$ because they do not belong to the domain of the function?
2026-03-29 04:44:08.1774759448
Should the critical points belong to the domain of $f$?
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Yes, you should exclude these points, since the domain of $f$ is $\{(x,y) \in \mathbb R^2: x >0,y>0 \}.$