Levantamento bibliográfico sobre o uso de derivadas para o estudo de máximos e mínimos com aplicações

Abstract

It is evident the significant presence of maximum and minimum problems in several aspects of everyday life and in the various areas of scientific knowledge. In view of this, the subject of derivatives was investigated, in order to understand its origin, its definition, and applications, which are essential in mathematical analysis to discern critical points, that is, where functions reach extreme values in the study of maxima and minima. Therefore, the general objective of this work is to understand the use of derivatives for the study of maxima and minima, and as specific objectives, to conceptualize derivatives, relate them to maxima and minima, and understand their applications in different areas of knowledge. The research was based on the contributions of renowned authors in the field of calculus, Newton and Leibniz, who were responsible for the emergence of the theory about derivatives, highlighting its practical applicability. Focusing on the usefulness of calculus, especially in maxima and minima, we aim to highlight its relevance in the academic context and analyze its application in different contexts. This understanding provides valuable tools to approach practical challenges in various spheres, highlighting the optimization of real problems. In this way, the research seeks to define derivatives, in order to explain their relationship with maxima and minima, aiming to understand their applications, showing that Mathematics is directly connected to other areas.