Extremal (source code)

= Extremal

A sufficiently regular admissible <function> at which the <first variation> of a <functional> vanishes for every permitted <variation>. An <extremal> is a stationary candidate; it need not be a local maximum or minimum. For a first-order integral <functional> with fixed endpoint values, it satisfies the <Euler-Lagrange equation> under the usual regularity assumptions.