# Activities

• • • ##### Subject Area

• Math: Calculus: Derivatives

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

• ##### Report an Issue

Derivative Function

#### Activity Overview

Transition from thinking of the derivative at a point to thinking of the derivative as a function.

#### Objectives

• Visualize the graph of a function’s derivative by considering the slope of the graph of the original function
• Relate increasing/decreasing behavior of the function to the sign of its derivative

#### Vocabulary

• slope of a tangent line
• derivative at a point
• derivative function

#### About the Lesson

This lesson involves making the transition from thinking of the derivative at a point (i.e., as a numerical value associated with the local slope at a particular location on the graph of a function) to thinking of the derivative as a function (by considering the numerical calculation as a process that can be employed across a domain). Students will use two familiar function examples (y = f(x) = x2 and y = f(x) = sin(x)).