Education Technology

# Activities

## Relating Graphs of a Function To Derivatives

#### Activity Overview

Students will be lead to discover the relationship between the graph of a function, graph of first derivative, and graph of the second derivative using TI-InterActive!™.

#### During the Activity

The attachments show the following functions: first derivative, and second derivative being graphed.

When first discovering the relationship, consider clicking on the graph and only showing two of the graphs at a time.

Also click on the functions below the graph. By hiding the input will help students' to focus on the graphs. Slide bars are for convenience in changing the functions to be graphed.

Again in the assessment all three graphs are shown. The questions are based on showing students the first derivative. Change questions and graphs to fit needs.

#### After the Activity

Extension: Use the graphs to relate to position, velocity, and acceleration.

Graph may also be changed to paramentric form. Graph x(t) = f(t) and y(t)=2 for example will help to illustrate a particle moving on a line.