Hi i am little sister of m777 my question is
if f(x,y) = 2xy - 5x^2 -2y^2 + 4x + 4y + y what are saddle point of this function?
so find partial derivatives of x and y. then set each of these equations equal to 0. Solve the solution set for x and y. this is your first critical point. Next, you want to calculate the 2nd partial derivative. So find (Fx)x and (Fy)y. Then find (Fy)x or (Fx)y, they are the same thing. You want to find the determinant using these 4 partial derivatives. you want to set it up like this:
| (Fx)x (Fx)y|
| (Fy)x (Fy)y|
so you have [(Fx)x * (Fy)y] - [(Fy)x * (Fx)y]
when you find this you will get some sort of equation. substitute all of your critical points into this equation you just found. the critical point that you substitute in and you get an answer that is negative, is your saddle point.