## The Second Derivative and the Shape of a Function f(x)

Read this section to learn how the second derivative is used to determine the shape of functions. Work through practice problems 1-9.

### Introduction

The first derivative of a function gives information about the shape of the function, so the second derivative of a function gives information about the shape of the first derivative and about the shape of the function. In this section we investigate how to use the second derivative and the shape of the first derivative to reach conclusions about the shape of the function. The first derivative tells us whether the graph of is increasing or decreasing. The second derivative will tell us about the "concavity" of , whether is curving upward or downward.

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-4.4-Second-Derivative.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.