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## Homework Statement

Find and characterise the stationary points for F(x,y,z) = x

^{2}+ xy + y

^{2}- 2z

^{2}+3x -2y +z

## The Attempt at a Solution

I found f

_{x}, f

_{y}, f

_{z}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?