Using GeoGebra to understanding of Implicit Derivatives in Engineering

Abstract

This article presents an educational intervention in the classroom for Univariate Mathematical Analysis, focusing on the concept of implicit derivatives and their graphical visualization using GeoGebra. The goal was to overcome the difficulties faced by Civil Engineering students in graphing implicit functions and understanding the relationship between the curve and its tangent line at a specific point, which hindered their geometric interpretation of the implicit derivative. The intervention was based on Raymond Duval's theory of semiotic representation registers, which suggests that students achieve a deeper understanding of a mathematical object when they can convert between different representation registers, in this case, from algebraic to graphical representation. An applet was designed in GeoGebra that allowed students to visualize implicit curves of the form  F(x,y)=0 and graph the tangent line at a given point. The methodology included using the applet to facilitate the transition from algebraic to graphical representation, allowing for a deeper understanding of the implicit derivative. The results showed a significant improvement in students' ability to understand the relationship between the algebraic expression of an implicit function and its graphical representation. It is concluded that integrating technological tools like GeoGebra, combined with the theory of representation registers, enhances the appropriation of abstract concepts like implicit derivatives by improving the ability to convert between different forms of mathematical representation.