Generalization of Lagrange’s Mean Value Theorem

Abstract

This paper deals with the mean value theorem of differential calculus due to the Lagrange’s mean value theorem which has appeared in Lagrange’s book Theories functions analytiques in 1797 as an extension of Rolle’s result from 1619. We state and prove a theorem which is similar to the generalized mean value theorem for the single variable function. Firstly, we review the mean value theorems. Moreover, the theorem is illustrated with some examples. The main propose of this paper is to establish the different forms of Lagrange’s Mean Value Theorem, as an extended forms.