D08 - Advanced Applications
Objectives & Resources
1. Understand that the derivative of a function has multiple interpretations and applications, including those that involve instantaneous rates of change. [EU 2.3]
2. Be able to solve a variety of problems, including rectilinear motion, related rates, optimization, and other advanced problems. [LO 2.3C]
a. Motion Problems: Know that the derivative can be used to solve rectilinear motion problems involving position, speed, velocity, and acceleration. [EK 2.3C1]
MOTION PROBLEMS
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EXPLORATION
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PRACTICE
TEXTBOOK 4.2 (page 209): 30. |
b. Related Rates Problems: Know that the derivative can be used to solve related rates problems, that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known. [EK 2.3C2]
RELATED RATES PROBLEMS
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PRACTICE
TEXTBOOK Lesson 4.6: Rates & Related Rates Exercises 4.6: #1, #3, #4, #7, #13, #15. |
c. Optimization Problems: Know that the derivative can be used to solve optimization problems, that is, finding a maximum or minimum value of a function over a given interval. [EK 2.3C3]
OPTIMIZATION PROBLEMS
Optimization Problems usually involve finding "extrema." This link provides a good description of local/relative maximum/minimum values as well as global/absolute maximum and minimum values.
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PRACTICE
TEXTBOOK 4.3 (p218): 2, 5, 6, 7, 10, 11. 4.1 (p199): 1, 2, 3, 4, 9, 16. REVIEW 4.2 (p209): 1, 2, 3, 10, 17. REVIEW |
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PRACTICE
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d. Other Applied Problems: Be able to solve problems involving rates of change in applied contexts by knowing that the derivative can be used to express information about rates of change in these contexts. [LO 2.3D and EK 2.3D1]
3. Make sense of problems and persevere in solving them. You will be able to ...
a. Understand the problem, find a way to tackle it, and work until it is done.
b. Analyze givens, constraints, relationships, and goals.
c. Make conjectures about the form and meaning of the solution, and plan a solution pathway rather than simply jumping into a solution attempt.
d. Check your answers to problems using common sense and alternative methods.
SAMPLE CONTENT ASSESSMENT ITEMS
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The Khan Academy and Textbook problems above are also good examples of possible assessment items.