(x,y) is a stationary point of a function f(x,y) if the surface z = f(x,y) has a horizontal tangent plane above (x,y). Equivalently, if ∂f/∂x = 0 and ∂f/∂y = 0. Now let
If rt>s2 and r<0, the stationary point is a local maximum; if rt>s2 and r>0, the stationary point is a local minimum; if rt<s2, the stationary point is a saddle-point. If rt = s2, then the stationary point is said to be degerenerate. See also Hessian.