Visualization of relationship between a function and Its derivative

Abstract

The first and second derivatives of a function provide an enormous amount of useful information about function itself as well as of the shape of the graph of the function. Mathematics curriculum in Bosnia and Herzegovina emphasises algebraic representation of a function ant its derivatives. That implies that concept of a derivative of a function is only partialy developed. On the other hand, an important skill to develop is that of producing the graph of the derivative of a function, given the graph of the function and conversely, to producing the graph of a function, given the graph of its derivative. In this paper we describe one possibility of enhancing pupils understanding of relationship between function and its derivative using specially designed Wolfram Mathematica applet. Preliminary results of implementation of the applet during the topic Examination of functions using its derivatives, indicate that visualization support better understanding of concept of function and its derivative.

Keywords

• Function, Derivative, Graphical representation

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