Continuity and differentiability of real functions: a proposal for the study of these notions with the use of the computer

Abstract

His paper aims at analyzing the use of computers when teaching differentiability and continuity in real-valued functions. The relation is approached in the case of a non-differentiable continuous real interval through an example is found in an article written by David Tall and is used to evidence a way in which a computer helps the learning and teaching of concepts of Differential and Integral Calculus when didactic and meaningful materials are produced. Elements of Tall’s theory on the advantages of the use of computers in Education, as well as the historical importance of the development of an example of a continuous non-differentiable function are presented in this paper. In addition, a case of a function defined as limit to a series of functions is explored. In addition, commands and tools, which are available in the software GeoGebra, are presented. As a result, we present tools, which will hopefully contribute to the practice as well as advancements in Mathematics Education at higher education level.