Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Applications of the Derivative

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Inflection Points

#### Activity Overview

Students investigate points of inflection on a function and its first and second derivatives, and discover how they relate to each other.

#### Key Steps

• Students will explore inflection points graphically and algebraically. They will use the graphs of the function and its first and second derivative to identify the inflection points.

• Next, students will use the information gained from the graph to identify points of inflection algebraically. Given a function and its first and second derivatives, students will solve the second derivative for zero to find possible inflection points. Students will then test the results to identify actual inflection points.