The continuous function f(x,y) is said to have saddle point at (a,b) if
where the subscripts x, y etc, denote partial derivatives.
fx(a,b) = fy(a, b) =0; fxy2 - fxyfyy < 0 at (a, b)
fx(a, b) = 0; fy(a, b) = 0; fxy2 - fxx . fyy > 0 at (a, b)
fx(a, b) = 0; fy(a, b) = 0; fxx and fyy < 0 at (a, b)
fx(a, b) = 0; fy(a, b) = 0; fxy2 - fxx = 0 at (a, b)