Analysis of extrema problems

Abstract

This document gathers a systematic analysis of function extrema problems. To do so, a previous introduction to the theory is made to understand and develop the results and examples contained in later sections. Concepts, notations and important results about single and multi variable calculus and general topology are included. Afterwards, the project is fundamentally divided in two sections: a first one focused on analyzing the methods to classify critical points of a function and a second one concentrated in the behavior of the quantity of extrema in single and multi variable functions.