NEKG33 Mathematical methods for economists

Chapter 8 : Day 08: Optimizing a function of one variable

By Lund University

We know how to differentiate a function. Let's use these mad skills to optimize a function.

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 necessary and sufficient conditions for max/min.

Single-variable optimization, definitions

Single-variable optimization, results

Single variable optimization: Problems

Exercises on single variable optimization

Problem: Maximize function

Problem: Find extreme points

Problem: Maximize function

Problem: Maximize function

Problem: Find extreme points

Problem: Find extreme points

Problem: Maximize function

Problem: Maximize/minimize function

Problem: Maximize profit

Problem: Maximize/minimize function

Problem: Maximize/minimize function over interval

Problem: Find local extreme points