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The Mean Value Theorem

In: MVT: A Most Valuable Theorem

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  • Craig Smoryński

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.

Suggested Citation

  • Craig Smoryński, 2017. "The Mean Value Theorem," Springer Books, in: MVT: A Most Valuable Theorem, chapter 0, pages 151-444, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-52956-1_3
    DOI: 10.1007/978-3-319-52956-1_3
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