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Local Linearization, 1st and 2nd Derivative Tests, and Computing Derivatives

# Local Linearization, 1st and 2nd Derivative Tests, and Computing Derivatives

Unit 9: Full Course Review via Motion

Lesson 3 of 17

Lesson 3 of 17

## Objective: SWBAT estimate points on a function using local linearity; SWBAT use the first and second derivative tests to identify local extrema; SWBAT differentiate functions using power, product, quotient and chain rules.

## Big Idea: We’ve justified interest in derivatives conceptually; we now review computing derivatives algebraically and some mathematical applications.

Subject(s):

Math, local linear approximation, Precalculus and Calculus, Derivatives, AP Calculus AB, AP Calculus, local linearization, 1st derivative test, first derivative test, 2nd derivative test, second derivative test

*120 minutes*

3

#### Setting the Stage

*15 min*

**Distribute the Limits Quiz - Course Review.** This is a no calculator quiz, and students should need just about 15 minutes to complete it.

**Resources**: Limits Quiz – Course Review

#### Resources

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6

Math Forum, discussion about l'Hospital's Rule

http://mathforum.org/library/drmath/view/53658.html

Google Form link (post online)

College Board Store, Released Multiple Choice Questions 1969-1998

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- UNIT 1: Back to School
- UNIT 2: Limits and Derivatives
- UNIT 3: Formalizing Derivatives and Techniques for Differentiation
- UNIT 4: Applications of Differentiation, Part 1
- UNIT 5: Applications of Differentiation, Part 2
- UNIT 6: The Integral
- UNIT 7: Applications of Integration
- UNIT 8: Differential Equations
- UNIT 9: Full Course Review via Motion
- UNIT 10: The Final Stretch - Preparing for the AP Exam

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- LESSON 1: Limits and l'Hospital
- LESSON 2: Know Your Limits
- LESSON 3: Local Linearization, 1st and 2nd Derivative Tests, and Computing Derivatives
- LESSON 4: Derivatives Algebraically and Graphically
- LESSON 5: The Calculus of Motion
- LESSON 6: Motion - Velocity on Intervals
- LESSON 7: Motion - Distance vs Displacement
- LESSON 8: Motion - With Multiple Derivatives
- LESSON 9: Motion and Optimization
- LESSON 10: Calculus and My Car's Dashboard
- LESSON 11: Rockin' Related Rates
- LESSON 12: Meet My Friend Riemann
- LESSON 13: Cookies and Pi
- LESSON 14: Accumulate This!
- LESSON 15: Wait, the Interval Width Varies?
- LESSON 16: Integrating Areas to Get Volumes
- LESSON 17: More Areas and Volumes

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