Question

Under what conditions on the constant k will the function f(x, y, z) = \(kx^2 + kxz - 2yz - y^2 +
\frac{k}{2} z^2\) have a non-degenerate local maximum at (0, 0, 0)?

Answer 1

you know when f has a non-degenerate local maximum ?

Answer 2

det(H) \(\ne\) 0
det(H) > 0
\(f_{xx} <0\)
Actually, I am not sure...

Answer 3

something like, condition for non-degenerate critical point p
\(\Large \det D^2(f)_p \ne 0\)
idk what that means, can you make something of this ?