The Mean Value Theorem

Craig Smoryński ()

Chapter Chapter 3 in MVT: A Most Valuable Theorem, 2017, pp 151-444 from Springer

Abstract: Abstract This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value Theorem and some of its variants, proofs of these results, their interrelations, and some applications. The second section provides to some extent the prehistory of the Mean Value Theorem, from Apollonius’s and Archimedes’s geometric proof for conic sections to Lagrange’s non-rigorous establishment via Taylor’s Theorem. Sections 3.3–3.8 then present the history of the development of the Mean Value Theorem itself from Lagrange’s weak version through the modern formulation by Bonnet. The rest of the chapter deals with the aftermath—its dissemination, generalisation, and failure to generalise in the Complex case.

Date: 2017
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DOI: 10.1007/978-3-319-52956-1_3

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