= Minimum locus of a squared function
{title2=$\underset{g=0}{\min}\,(g^2-c)=-c$}
If a real-valued <function> $g$ has a zero in the feasible region, then $g^2-c\geq-c$, with equality precisely on that zero set. The minimum can therefore occur along a curve or a higher-dimensional set rather than at isolated <critical points>. To maximize it on a compact feasible region, maximize $|g|$: both the largest and the smallest values of $g$ must be considered, since a large negative value also has a large square.
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