# Der. App Word Problems

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

**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 b2003 (Form B) Q4 - Given

*v*(*t*) as an equation - parts a, b, and c2002 Q3 - Given

*v*(*t*) as an equation - part a and b2000 Q2 - Given

*v*(*t*) as a graph and as an equation - parts a & b1999 Q1 - Given

*v*(*t*) as an equation - parts a & b1998 Q3 - Given

*v*(*t*) as an equation and as a table - parts a, b and c

### Optimization

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

Explanation:

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

**9) Related Rates**

Explanation:

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:

Practice Problems: