= Maximum and minimum
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= Extremum of a real-valued function
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= Extremum
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= Extrema
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Maxima and minima are <extrema> of a real-valued function. A global maximum of $f$ on its domain $D$ is a point $x_*$ with $f(x)\leq f(x_*)$ for every $x\in D$; a global minimum reverses the inequality. A local extremum requires the inequality only in a <neighbourhood> of the point within $D$. In <constrained optimization>, $D$ is the feasible set, so an extremum is tested relative to the constraints rather than in every ambient direction. Thus a constrained <local maximum> or <local minimum> can occur at a boundary point without being an interior <critical point>.
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