- #1
trap101
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So I am solving for the critical points of x3-3x-y2+9y+z2
I've found the critical points and I'm just evaluating them in the Hessain. Now I computed the eigenvalues for the hessian, but one of my 2nd order derivatives was a constant. So my hessian looked like this (it was diagonal, so I'm only writing the diagonal terms)
(6x - λ), (-6y-λ), (2-λ)
Now all my C.P were of the form (±1,±√3,0)
So whatever eigenvalues I solve for I am always going to get λ=2, but in the solutions they said that a maximum existed at (-1,√3,0) but if I solve for the eigenvalues I will have λ = -6, λ = -6√3, λ = 2. So how is this a local max if they are not all negative. (long winded for short explanation I know)
I've found the critical points and I'm just evaluating them in the Hessain. Now I computed the eigenvalues for the hessian, but one of my 2nd order derivatives was a constant. So my hessian looked like this (it was diagonal, so I'm only writing the diagonal terms)
(6x - λ), (-6y-λ), (2-λ)
Now all my C.P were of the form (±1,±√3,0)
So whatever eigenvalues I solve for I am always going to get λ=2, but in the solutions they said that a maximum existed at (-1,√3,0) but if I solve for the eigenvalues I will have λ = -6, λ = -6√3, λ = 2. So how is this a local max if they are not all negative. (long winded for short explanation I know)