Solution
= Solution
The <gradient> vanishes at the origin. Its <Hessian matrix> there is
$$
H=\begin{pmatrix}0&1\\1&0\end{pmatrix},
$$
with <eigenvalues> $1$ and $-1$. The quadratic term is therefore indefinite, so the origin is a \b[<saddle point of a scalar function>]. Equivalently, the leading term $xy$ is positive along $y=x$ and negative along $y=-x$.