# Der. App Word Problems

**Motion Problems: Position, Velocity, and Acceleration**

**1) Relationship of position, velocity, and acceleration and applied extrema.**

**2) Speed increasing/decreasing and moving away/towards the origin.**

- Explanation:
- Quizlet flashcards
- Video (from Hollis) - watch until 12:25

- Practice Problems:

**3) Interpreting the graph of motion functions**

**4) AP Free Response Questions**

- AP questions: Motion along a line WS â€“ derivatives only
- 2010 (Form B) Q6 - Given a position equation - parts a, b, and c
- 2010 (Form B) Q4 - Given
*v*(*t*) as a graph - part a and b

- 2007 Q4 - part a
- 2005 (Form B) Q3 - parts a and b
- 2004 Q5 - parts a, b, and c
- 2003 Q2 - Given
*v*(*t*) as an equation - parts a and b - 2003 (Form B) Q4 - Given
*v*(*t*) as an equation - parts a, b, and c - 2002 Q3 - Given
*v*(*t*) as an equation - part a and b - 2000 Q2 - Given
*v*(*t*) as a graph and as an equation - parts a & b - 1999 Q1 - Given
*v*(*t*) as an equation - parts a & b - 1998 Q3 - Given
*v*(*t*) as an equation and as a table - parts a, b and c

**5) Derivative Review **

**6) Applied Max./Min. Problems or Optimization Problems**

- Explanation:
- Notes | Annotated
- Notes #2
- Example
- Videos:
- Worldwide Center of Mathematics: Optimization (best example at 46:50
- Hollis: applied optimization problems: slides 1, 3, and 4 (slide 2 is more advanced)
- Khan: Optimization with Calculus 1: minimize x^2 + y^2 if xy = -16
- Khan: Optimization with Calculus 2: open box problem
- Khan: Optimization Example 4: minimum cost of an open box

- Websites: Optimization Problems from Visual Calculus: website with to help with visualization
- Java applets illustrating the solution to finding the maximum area of a rectangle which can be inscribed in a semicircles
- Java applet illustrating the solution to finding the longest ladder which can be carried through a hallway with a corner.
- Java applet illustrating the solution to finding the shortest time to move through the desert to a town.
- Java applet illustrating the solution to finding the shortest ladder that can lean over a fence against a building.

- Practice Problems

**Related Rates**

8) Review Implicit Differentiation with respect to *t* Notes | Annotated

9) Related Rates Notes | Annotated | Related Rates WS #1 | Answers

10) Related Rates with Multi-step Problem Solving Notes | WS #2 | Answers

11) Related Rates: Cylinders and Cones Notes | Annotated | WS #3 | Answers

- Website: Animated gifs or quicktime movies that are visually represented of different related rates problems
- Videos:
- Hollis (start watching at 9:50 to 13:11 and 16:45-20:13)
- Worldwide Center of Mathematics: related rates (41:53)
- Khan Video: Rates of change (part 2): area of expanding circle
- Khan Video: Ladder rate of change problem
- Khan Video: Introduction to rate-of-change problems: cone problem

- AP Free Response:
- AP Free Response Questions (old) WS
- 2008 Q3 - parts a & b
- 2007 Q5 - part b
- 2003 Q5 - part a
- 2002 (Form B) Q6
- 2002 Q5

**12) Word Problem Review: Worksheet**

**Finals Review:** in addition to previous review worksheets, here is one more