Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Applications of the Derivative

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Report an Issue

Cubic, Zeros and Tangents

#### Activity Overview

In this Computer Algebra System (CAS) activity, students use CAS to prove a theorem regarding cubic functions, their zeros [roots], and tangents to the curves.

#### Before the Activity

• Install TI Connect™ using the TI connectivity cable
• See the attached PDF file for detailed instructions for this activity
• Print the attached PDF file for the class
• #### During the Activity

Distribute the page to the class.

• Graph a cubic function and find its roots
• Graph the tangent line at the average of two of these roots
• Determine the root of the tangent line
• Graph the tangent line at the average of two roots [different from the roots used earlier]
• Observe that in each case, the tangent line at the average of two of the roots appears to go through the other root of the cubic function
• Repeat the steps with other third degree polynomials
• Check if the pattern continues
• Make a conjecture and prove it using CAS on the calculator
• #### After the Activity

Students' answer questions on the Activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary