mean value theorem

Noun

Meaning

(mathematics) Any of various theorems that saliently concern mean values.

(calculus, uncountable) The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.

Synonyms

Examples

Cauchy's mean value theorem Cauchy's mean value theorem, also known as the extended mean value theorem, is a generalization of the mean value theorem. Source: Internet

If one uses the Henstock–Kurzweil integral one can have the mean value theorem in integral form without the additional assumption that derivative should be continuous as every derivative is Henstock–Kurzweil integrable. Source: Internet

If we place and we get Lagrange's mean value theorem. Source: Internet

In other words, : In practice, what the mean value theorem does is control a function in terms of its derivative. Source: Internet

Proof of Cauchy's mean value theorem The proof of Cauchy's mean value theorem is based on the same idea as the proof of the mean value theorem. Source: Internet

Mean value theorem for vector-valued functions There is no exact analog of the mean value theorem for vector-valued functions. Source: Internet

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