For f(x,y) = x^2 + y^2 + 3xy I need to find the critical points and prove whether or not they are local minima, maxima or saddle points. I thought the only critical point was (0,0) since Df = (2x + 3y, 2y + 3x) = 0. Doesn't this make (0,0) a local min? The reason I doubt this now is because upon constructing the Hessian matrix and finding the eigenvalues, I got lambda = 5 and -1 (which would show that the point is a saddle point). Can someone please help me with this?