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The First Derivative Test

# The First Derivative Test

Unit 3: Formalizing Derivatives and Techniques for Differentiation

Lesson 17 of 21

Lesson 17 of 21

## Objective: SWBAT use the 1st derivative test to classify local extrema and sketch functions.

## Big Idea: We have used multiple derivative relationships to identify a function’s extrema graphically. Now, let’s develop an algebraic approach.

Subject(s):

Math, Derivatives, calculus ab, first derivative test, local extrema, relative extrema, calculus, AP Calculus, AP Calculus AB

*60 minutes*

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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: Sketching Derivative Functions (Part 1 of 2)
- LESSON 2: Sketching Derivative Functions (Part 2 of 2)
- LESSON 3: Sketching Antiderivative Graphs (Part 1 of 2)
- LESSON 4: Sketching Antiderivative Graphs, In The Lab
- LESSON 5: Sketching Antiderivative Graphs (Part 2 of 2)
- LESSON 6: Multiple Representations of Multiple Derivatives
- LESSON 7: Introducing the Power Rule
- LESSON 8: The Product and Quotient Rules
- LESSON 9: Gettin' Triggy Wit It
- LESSON 10: The Chain Rule
- LESSON 11: Chain Rule Continued
- LESSON 12: Chain Chaaain Chaaaaaiin
- LESSON 13: Differentiation - The Next Level
- LESSON 14: Finding Local and Absolute Extrema (Part 1 of 3)
- LESSON 15: Finding Local and Absolute Extrema (Part 2 of 3)
- LESSON 16: Finding Local and Absolute Extrema (Part 3 of 3)
- LESSON 17: The First Derivative Test
- LESSON 18: The First and Second Derivative Tests
- LESSON 19: Differentiation Practice and Review (Part 1 of 3)
- LESSON 20: Differentiation Practice and Review (Part 2 of 3)
- LESSON 21: Differentiation Practice and Review (Part 3 of 3)

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