Unit 3

Prereq Test 3

Intro

The previous unit was all about the mathematical understanding of derivatives and how to calculate derivatives. This unit's focus is all about applying that understanding and calculations of derivatives to specific contexts and applications.

Overview 3

Inquiry Activity 3

Key Terms

Unit 3 Podcast (coming soon)

3.1 Using Derivatives to Determine Values

3.1.1 L'Hospital's Rule*

3.1.2 Linear Approximation*

3.2 Graphing and Derivatives

3.2.1 Increasing/Decreasing Intervals

3.2.2 Concavity

3.2.3 Mean Value Theorem

3.3 Modeling

3.3.1 Derivative in Context*

3.3.2 Related Rates

3.3.3 Optimization

3.3.4 Straight-Line Motion*

3.3.5 Parametric and Vector-Valued Motion Equations**

3.1 Videos

3.1.1 L'Hospital's Rule

- Conceptual Videos
  - L'Hospital's Rule
    - Video 1 - https://youtu.be/aH68iV_mwrA
    - Video 2 - https://youtu.be/W4S2inVRpTc
- Example Videos
  - Video 1 - https://youtu.be/kH65bI50xmw
  - Video 2 - L'Hospital's Rule (example problem 2)
  - Video 3 - https://youtu.be/7L2W66JSWK4

3.1.2 Linear Approximation

Conceptual Videos
- https://youtu.be/iGNHbJtngfk
Example Videos
- Video 1 - https://youtu.be/dCxCzLNWZU4
- Video 2 - https://youtu.be/Cx3rN5i8buI

3.2 Videos

3.2.1 Increasing/Decreasing Intervals

- Conceptual Videos
- Example Videos
  - Extrema (example problem 1 of 4)
  - Extrema (example problem 2 of 4)
  - Extrema (example problem 3 of 4)
  - Extrema (example problem 4 of 4)
  - Increasing and Decreasing Functions and Extrema (example problem 1)
  - Increasing and Decreasing Functions and Extrema (example problem 2)
  - Increasing and Decreasing Functions and Extrema (example problem 3)
  - Increasing and Decreasing Functions and Extrema (example problem 4) - https://youtu.be/MISVgrXEzxs

3.2.2 Concavity and Inflection Points

- Conceptual Videos
  - Concavity and Inflection Points (conceptual)
- Example Videos
  - Concavity and Inflections Points - https://youtu.be/JliehI4MuW4

3.2.3 Mean Value Theorem

- Conceptual Videos
- Example Videos
  - Mean Value Theorem Example Problem - https://youtu.be/oFYHvU04pzk

3.3 Videos

3.3.1 Derivative in Context*

Conceptual Videos
Example Videos

3.3.2 Related Rates

Conceptual Videos
Example Videos

3.3.3 Optimization

Conceptual Videos
Example Videos

3.3.4 Straight-Line Motion*

Conceptual Videos
Example Videos

Supplementary Practice

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