# Neke generalizacije Lagrangeovog teorema srednje vrijednosti

Matika, Monika (2015) Neke generalizacije Lagrangeovog teorema srednje vrijednosti. Diploma thesis, Faculty of Science > Department of Mathematics.

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## Abstract

In this paper we studied the mean value theorems and theirs generalizations. First we considered Lagrange’s, Rolle’s, Cauchy’s and Flett’s mean value theorem for real-valued functions of a real variable and showed their geometric interpretations. Furthermore, we gave examples to illustrate how we can use these theorems in solving problems. After that, we considered the mean value theorems and theirs generalizations for the functions of several variables, first for the real-valued functions of several real variables, then for the vector valued functions of one real variable and, finally, for the vector-valued functions of several real variables. In addition, we gave an example to illustrate that the mean value theorem cannot be directly extended in this more general situation. Finally, we discussed the mean value theorem for the complex-valued functions of a complex variable.

Item Type: Thesis (Diploma thesis) Arambašić, Ljiljana 2015 47 NATURAL SCIENCES > Mathematics Faculty of Science > Department of Mathematics Iva Prah 05 Jun 2015 11:13 05 Jun 2015 11:13 http://digre.pmf.unizg.hr/id/eprint/4013