Education Technology

MVT for Derivatives

Subject Area
Math: Calculus: Derivatives
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
45 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
4.5
Resource Types
Lessons
Format
TNS

MVT for Derivatives

Activity Overview

The MVT relates the average rate of change of a function to an instantaneous rate of change.

Objectives

  • Interpret the statement of the Mean Value Theorem in terms of its graphical representation
  • Use slopes of secant and tangent lines to explain the relationship between average and instantaneous rates of change demonstrated by the MVT
  • Identify functions and/or intervals for which the MVT cannot be applied

 

Vocabulary

  • secant line
  • tangent line
  • average rate of change
  • instantaneous rate of change

About the Lesson

This lesson uses a graphical representation of the Mean Value Theorem (MVT) to demonstrate how the theorem relates information about the average rate of change of a function to an instantaneous rate of change. As a result, students will:

  • Change the endpoints of intervals and relate the changes in the slopes of secant lines to the average rate of change.
  • Observe that for the first two functions provided there is always a point in the intervals where the tangent line is parallel to the secant line connecting the endpoints, supporting the conclusion of the MVT.
  • Observe a function that is not everywhere differentiable to note when the conclusion of the MVT may not hold.
Subject Area
Math: Calculus: Derivatives
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
45 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
4.5
Resource Types
Lessons
Format
TNS
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