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Minimal value of an 3 variable quadratic function

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April 23, 2009
quadraticsfunction

Problem Statement

x,y,z∈R x,y,z\in \mathbb R, find the minimal value of f(x,y,z)=2x2+5y2+10z2−2xy−4yz−6zx+3 f\left(x,y,z\right) = 2x^{2} + 5y^{2} + 10z^{2} - 2xy - 4yz - 6zx + 3.
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> −3<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ -3 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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