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The Mean Value Theorem

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More Calculus of a Single Variable

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

The main focus of this chapter is the Mean Value Theorem and some of its applications. This is the big theorem in the world of differentiable functions. Many important results in calculus (and well beyond!) follow from the Mean Value Theorem. We also look at an interesting and useful generalization, due to Cauchy.

Up the airy mountain, Down the rushy glen …

– The Fairies, by William Allingham

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Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State, Buffalo, NY, USA

    Peter R. Mercer

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  1. Peter R. Mercer
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Mercer, P.R. (2014). The Mean Value Theorem. In: More Calculus of a Single Variable. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1926-0_5

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