Aproximações de Funções usando Derivação

Abstract

The present research is a study about function approximations using derivation methods, since, during the teaching of calculus, we come across several functions with complex formulas that become problematic because they need more attention. Therefore, we aim to review essential concepts of calculus such as limit and tangent line, with a view to understanding the concept and the use of the derivative of a function to find expressions and approximate values of these functions in certain values. The methodology adopted is based on a fully bibliographic quantitative research, reviewing books, academic articles and lecture notes. It was found that the concepts of differentials can be developed in order to find approximate values of roots that strongly resemble their real values. In parallel, it is seen that the derivative of a function at a given point brings arbitrarily good estimates, and that the smaller the chosen parameters, the smaller the error. Furthermore, approaching the same concept, Taylor polynomials show us that an even closer approximation of the values of a function through derivation is possible.