Continuous functions and their derivatives

Abstract

The derivative of a function is a central concept that is approached in the upper secondary and higher education levels in Mexico. This concept is closely linked to the principle of function and instrumental in numerous situations where it is essential to analyze the changes of the variables involved. As an example, derivatives are crucial in the study of motion and velocity, the optimization of functions and obtaining straight lines. This didactic dissertation focuses on the concepts of function, derivative, geometric interpretation and determination of maxima and minima. The main goal is to demonstrate a few properties of this function type through theorems and to lay out a set of problems and exercises associated to these concepts. Hopefully, our readers will find interest and usefulness in the theoretical study of derivatives and their application in practical situations.