Let f(x,y). Points where both Fx(x,y) = Fy(x,y) = 0 are critical points, and will include any extrema or minima there. (KIM that extrema can occur at the boundary points of the region of f)
If a,b is such a point, D(a,b) will tell us if that point is either a local max, local min or a saddle point.