The function $g(s,t) = s^3 + 6st + 3t^2 - 9s + 2$...
... has no critical points.
... has four critical points: $(3, -3)$, $(-1, 1)$, $(3, 1)$ and $(-1, -3)$.
... has two critical points: $(3, -3)$ and $(-1, 1)$.
... has two critical points: $(-3, 3)$ and $(1, -1)$.