UMA ABORDAGEM GEOMÉTRICA DO CONHECIDO TEOREMA DO VALOR MÉDIO PARA FUNÇÕES REAIS DE DUAS VARIÁVEIS

Abstract

In this work we present a original approach to two known theorems of differential calculus. We discuss Rolle's Theorem and the Mean Value Theorem for real functions of two real variables. We show that such theorems are obtained by adapting the ideas from the proofs of these results in the case of functions of a real variable. Furthermore, we obtained an application of Rolle's Theorem, which relates the Gaussian curvature of a surface in R³ given by a graph of a function with the existence of closed level curves.

Keywords: Mean Value Theorem; Real function of two variables; Calculus.