The Derivative of a Function

Abstract

Starting from the problem to define the tangent to the graph of a function, we introduce the derivative of a function. Two points on the graph can always be joined by a secant, which is a good model for the tangent whenever these points are close to each other. In a limiting process, the secant (discrete model) is replaced by the tangent (continuous model). Differential calculus, which is based on this limiting process, has become one of the most important building blocks of mathematical modelling.