The role of the Darboux property in the core theorems of Calculus

Authors

  • Fernando Adrian Fernandez Tojo

DOI:

https://doi.org/10.1285/i15900932v45n1p57

Keywords:

Darboux function, Rolle's theorem, Lagrange's mean value theorem, Cauchy's mean value theorem, Taylor's theorem

Abstract

In this article we explore the role of the Darboux property in proving some of the basic results of Mathematical Analysis, such as Rolle's theorem, Lagrange's mean value theorem, Cauchy's mean value theorem or Taylor's theorem. We show that the classical hypotheses used to prove these theorems can be relaxed.

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Published

08-09-2025

Issue

Volume 45, issue 1 (2025)

Section

Articoli

License

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode