Solution
= Solution
Translate the coordinates by $u=x-1$ and $v=y+1$, and write $E=e^{-(u^2+v^2)/2}>0$. The <partial derivatives> are
$$
f_x=v(1-u^2)E,\qquad f_y=u(1-v^2)E.
$$
If $u=0$ or $v=0$, these equations together force $u=v=0$. Otherwise they require $u^2=v^2=1$. Thus the complete set of <stationary points> is
$$
\boxed{(x,y)=(1,-1),\ (2,0),\ (0,-2),\ (2,-2),\ (0,0).}
$$