## Mathematics for Economists

## Chapter 6 : Single variable optimization

### By Lund University

In this chapter we will look at how to maximize or minimize a function of one variable. There is not much theory in this chapter, the best way of learning how to optimize functions is through lots of problems.

## Single variable optimization

We begin this section by looking at concepts related to single variable optimization. We distinguish between local extreme points and global extreme points and we introduced the concept stationary point (when the derivative is zero). We continue with some important results related to single variable optimization such as the first and the second derivative tests (necessary and sufficient conditions) and the extreme value theorem. In the final lecture we introduce inflection points, points where the function goes from being convex to concave or vice versa.

#### Single-variable optimization, definitions

#### Single-variable optimization, results

#### Inflection points

## Single variable optimization: Problems

Exercises on single variable optimization