second mean-value theorem

[¦sek·ənd ¦mēn ¦val·yü ‚thir·əm] (mathematics) The theorem that for two functions ƒ(x) and g (x) that are continuous on a closed interval [a, b ] and differentiable on the open interval (a, b), such that g (b) ≠ g (a), there exists a number x₁ in (a, b) such that either [ƒ(b) - ƒ(a)]/[g (b) -g (a)] = ƒ′(x₁)/ g ′(x₁) or ƒ′(x₁) = g ′(x₁) = 0. Also known as Cauchy's mean-value theorem; double law of the mean; extended mean-value theorem; generalized mean-value theorem.

单词	second mean-value theorem
释义	second mean-value theorem second mean-value theorem [¦sek·ənd ¦mēn ¦val·yü ‚thir·əm] (mathematics) The theorem that for two functions ƒ(x) and g (x) that are continuous on a closed interval [a, b ] and differentiable on the open interval (a, b), such that g (b) ≠ g (a), there exists a number x₁ in (a, b) such that either [ƒ(b) - ƒ(a)]/[g (b) -g (a)] = ƒ′(x₁)/ g ′(x₁) or ƒ′(x₁) = g ′(x₁) = 0. Also known as Cauchy's mean-value theorem; double law of the mean; extended mean-value theorem; generalized mean-value theorem.
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