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单词 global maximum
释义

global maximum

(global minimum) A global maximum (resp. minimum) for a real function on a set X is a value f (x0) such that f (x) ≤ f (x0) for all x (resp. f (x) ≥ f (x0) for all x). The function f (x) = x3−3x on the interval [0,2] has a global minimum of −2 achieved at x = 1 which, being an interior point, is also a stationary point by Fermat's Theorem. f(2) = 2 is a global maximum which is not a stationary point and f (0) = 0 is a local maximum which is not global and is not stationary. See also Weierstrass theorem.

The extrema of f(x)

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更新时间:2025/4/30 3:42:39