Solution
= Solution
$\nabla U=(3x^2-3+y^2,2y(x+1))$, so the <critical points> are $(\pm1,0)$. The <Hessian matrix> at $(1,0)$ is $\operatorname{diag}(6,4)$, making it the <local minimum>; $(-1,0)$ is degenerate and not a minimum.
= Solution
$\nabla U=(3x^2-3+y^2,2y(x+1))$, so the <critical points> are $(\pm1,0)$. The <Hessian matrix> at $(1,0)$ is $\operatorname{diag}(6,4)$, making it the <local minimum>; $(-1,0)$ is degenerate and not a minimum.