# Chapter 12 Optimization

This module is based on Chapter 12 in the textbook. Each section includes a workbook and the answer to the practice exercises are available below.

In the last chapter, you learned how to measure change using derivatives. Now that you know how to take a derivative and interpret the results, we want to be able to apply derivative to solving more business problems.

We’ll start out this module by tracking the sign of the derivative. This will help us to determine when he function is increasing and when it is decreasing. When the derivative is positive, the tangent line has a positive slope and the function is increasing. A negative derivative means the slope of the tangent line is negative so the function must be decreasing.

At the end of the module, we’ll analyze business functions such as profit, revenue and average cost. This will help us to determine the production level that maximizes profit or revenue and the production level that minimizes average cost.

Section 1 – Extrema of a Function

Section 2 – Higher Derivatives

Section 3 – Optimizing Business Functions

Section 4 – Business Applications of Extrema