Find and characterise the stationary points for F(x,y,z) = x2 + xy + y2 - 2z2 +3x -2y +z
The Attempt at a Solution
I found fx, fy, fz and let them equal to 0. Solving gives me the critical point (-8/3,7/3,14). From here I'm not sure how to determine the nature of this critical point. I know how to check given a two variable function, but for 3 I am a bit stuck. I think I have to find the determinant of the Hessian with all second derivative entries but is there an easier way than this?