A proposal of activities for the understanding of the derivative in optimization problems

Abstract

This paper intends that, through optimization problems, the student will be able to reach an understanding of the notion of derivative. For this purpose, an activity is proposed, which consists in the student solving an optimization problem from different representation registers and justifying each one of his or her procedures, this will allow him or her to show the implication of the derivative in the resolution of the proposed problem. The use of the different representation registers for the solution of the proposed problem agrees with the different ways of solving an assignment, which are defined as techniques in a mathematical praxeology. In this way, the a priori analysis of this work is done considering the Theory of Registers of Semiotic Representation and the Anthropological Theory of Didactics.