Derivative, maxima and minima in a graphical context

Abstract

A deeper learning of the properties and applications of the derivative for the study of functions may be achieved when teachers present lessons within a highly graphic context, linking the geometric illustrations to formal proofs. Each concept is better understood and more easily retained when it is presented and explained visually using graphs. In this article, we explore the conditions of necessity or sufficiency of the criteria for determining the maxima and minima of a function. The implications for the teaching of derivatives and functions in undergraduate courses are discussed in light of our analysis of textbooks.

Keywords:

• undergraduate courses
• calculus
• derivative
• critical point, maxima
• minima

Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the quality of this article. Also, particular thanks to Kelly E. Matthews, Lecturer in Higher Education at the University of Queensland (Australia), for her insightful and thoughtful comments.

Notes

Note

1. Consider: To think about carefully. Merriam Webster Dictionary 2011.