5.1 Introduction

You may have studied a type of financial security called derivatives in a business or finance course. The concept of derivatives in math is not so different.

A derivative in math is the instantaneous rate of change of a function with respect to input variables. This is an important concept in business. For example, what is the additional profit to your company if it sells 1 extra unit, or 1,000 extra units? You might think that this profit function should be linear. However, the company can charge less to acquire more customers since each one has a different amount that they are willing to pay for the same product. In addition, the cost of manufacturing the product may be reduced as the company operates on a larger scale, as it may be able to secure purchase discounts on bigger orders of raw materials.

This topic will help you learn how to optimize business decisions given mathematical formulas.