Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation

We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem fa-f(b)b-a=f'(c)$ \frac{f(a)-f(b)}{b-a}={f}^{\prime}(c)$we provide the expression of its gradient ∇c(d,d), thus giving the asymptotic behavior of c(a, b) when...

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Bibliographic Details
Main Author: Hiriart-Urruty Jean-Baptiste
Format: Article
Language:English
Published: EDP Sciences 2021-08-01
Series:ESAIM: Proceedings and Surveys
Online Access:https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107110.pdf