Cauchy mean-value theorem

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Cauchy mean-value theorem [kō·shē ¦mēn ¦val·yü ‚thir·əm]

(mathematics)

The theorem that if ƒ andgare functions satisfying certain conditions on an interval [a,b], then there is a pointxin the interval at which the ratio of derivatives ƒ′(x)/g′(x) equals the ratio of the net change in ƒ, ƒ(b) - ƒ(a), to that ofg.

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