Abstract
In this chapter, which is independent of all subsequent chapters, we allow ourselves a brief diversion. We have met and used Rolle’s Theorem (Theorem 5.1), its extension the Mean Value Theorem (Theorem 5.2), and its extension Cauchy’s Mean Value Theorem (Theorem 5.11). Here we consider other Mean Value – type theorems. Each of these, as with their namesake, has an appealing geometric interpretation.
One cannot fix one’s eyes on the commonest natural production without finding food for a rambling fancy.
—Mansfield Park, by Jane Austen
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Mercer, P.R. (2014). Other Mean Value Theorems. 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_7
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DOI: https://doi.org/10.1007/978-1-4939-1926-0_7
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