Revisiting the Derivative: Implications on the Rate of Change Analysis

The aim of this paper is to raise concerns with the mathematical concept of the derivative as we know it. It raises concerns of accuracy. The paper is kept as simple as possible, solutions are always meant to be as simple as possible to be easily understood. The paper looks at linear and polynomial functions to illustrate that the derivative is not as precise as it should be, and in some instances can be considered almost a relic, though the solutions that are derived consider the simple derivative. It is the nature of polynomial functions that lead to the derivative not to be accurate and this paper clearly shows the shortcomings. The paper ends with a derivative that is accurate and precise, a derivative that when broken down is so simple. The main lesson/ conclusion is that it is all in the function, complex derivatives are not always necessary. This has important implications to all researchers, scientists who use the derivative to predict.