Consider the function $f(x,y) = x^{2}y+y^{3}-12y$.

$f$ has ? a maximum a minimum a saddle some other critical point no critical point at $\left(0,-2\right)$.

$f$ has ? a maximum a minimum a saddle some other critical point no critical point at $\left(0,0\right)$.

$f$ has ? a maximum a minimum a saddle some other critical point no critical point at $\left(-2\sqrt{3},0\right)$.

$f$ has ? a maximum a minimum a saddle some other critical point no critical point at $\left(2\sqrt{3},0\right)$.

$f$ has ? a maximum a minimum a saddle some other critical point no critical point at $\left(0,2\right)$.