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Optimizing Quadratic Functions with the Second Derivative Test
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[QUOTE="Zyuke, post: 4468630, member: 485230"] Under what conditions on the constants a and b does the second derivative test guarantee that the function g(x,y,z)=ax^2+2axz+by^2-2byz+z^2 has a local maximum at (0,0,0)? a local minimum at (0,0,0)? well, i used the Hessian matrix to compute the eigenvalues to set them above zero. but the computation is so complicated that i used Mathematica to solve them and it turned out to be some messy stuff. i was convinced that this is not the way to do it. but then how? [/QUOTE]
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Optimizing Quadratic Functions with the Second Derivative Test
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