# Extrema of a Function

Many applications in business and economics require us to find either the highest point or the lowest point on a function. If we have a function that describes volume of a piece of luggage as a function of its dimensions, the highest point on the graph gives us the dimensions at which the volume is greatest. For a product’s average cost function, the lowest point on the function gives us the production level that yields the lowest cost per unit.

In this section we’ll find these points by learning how to find the bumps and dips on a function’s graph as well as the very highest and lowest points on a graph.

**Read **

- What is the difference between a relative extremum and an absolute extremum?
- What is a critical point of a function?
- How do you find the relative extrema of a function?
- How do you find the absolute extrema of a function?
- Handout: Increasing / Decreasing Exponential
- Handout: Increasing / Decreasing Polynomial
- Handout: Absolute Extrema Application

Section 12.1 Workbook (PDF) – 9/5/19

**Watch **Video Playlist