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Alignment
- Standards Alignment
- Textbook Alignment
Subject Area
- Math: Calculus: Derivatives
Author

Texas Instruments
Level

9-12
Activity Time

15 Minutes
Device
- TI-Nspire™ Navigator™
- TI-Nspire™
- TI-Nspire™ CAS
Software

TI-Nspire™
TI-Nspire™ CAS
TI-Nspire Version

2.0
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Secant and Tangent Lines

Activity Overview

In this activity, students will observe the slopes of the secant line and tangent line as point Q on the function approaches the other point P. They will also determine the average rate of change for an interval and approximate the instantaneous rate of change using the slope of the secant line.

Key Steps

In this activity, students will explore secant and tangent lines of the graph y = x² visually by grabbing point Q and moving it toward point P. They are asked to make an observation about the lines and the values of the slopes.
Students are asked to determine the value of the average rate of change of f1(x) on the interval [1, 1.1] using the graph and table of values. They will then write and calculate an expression to estimate the instantaneous rate of change of f1(x) at x = 1.

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Secant and Tangent Lines

Activity Overview

Key Steps

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