# Project 2: Derivatives

## Instructions

Use Winplot and Google Docs to create a document with four problems on it. The problems should be similar to those in the book, but don't work out the indicated problems.

## Problem 1: Matching

Create a problem similar to problem 2.2.3 with four graphs and four derivatives. Notes: This would be a good time to use a Winplot image size of 8.1 cm, then you can fit two graphs side by side. Make sure all graphs are centered at the origin so that the viewing window doesn't give away the answer. Hide the scale labels on the axes.

## Problem 2: Derivatives from a Table

Create a problem similar to problem 2.5.55 that includes some questions that require the use of the addition/subtraction rule, product rule, quotient rule, and chain rule. Include 8 parts. You will probably also need to include more than 3 values of x, and you are certainly not limited to the values 1, 2, and 3 like problem 2.5.55. You can use any integer values for x, they do not need to be consecutive.

## Problem 3: Implicit Differentiation

Create a problem similar to problems 2.6.19-24 and 2.6.29-32.

Type the equation of the relation and include a graph in the question itself (rather than making part of the instructions be to graph the curve).

In the graph you make for the solution, include the tangent lines at the points you picked. Problems 19-24 and 29-32 include a lot of different things; what I'm mainly after are for you to (a) ask about the number of horizontal tangents and the coordinates where they occur and (b) pick a few points on the curve and find equations of tangent lines at those points. No more than one of them should be a horizontal tangent.

## Problem 4: Pursuit Curve

Answer this question: A thief steals a ladies purse and takes off running north at a rate of 7 feet per second. A former high school football cornerback is standing 200 feet due east of the lady, sees the robbery, and immediately takes off running towards the thief at 12 feet per second. The purse rescuer continually adjusts his direction so that he is running directly towards the attacker. For a visualization, visit the Pursuit Curve at MathWorld.

1. Create a Google Spreadsheet and share it with your group (and anyone with the link). Start with time t=0 seconds and use an increment of dt=0.5 seconds to create a spreadsheet that calculates the coordinates of the attacker and the rescuer at time t. Hint: you are essentially stringing local linear approximations together to recreate a curve. Insert a scatterplot to show the path followed by the rescuer. The rest of the questions should be answered in your main document.
2. How quickly is the distance between the thief and the hero changing at t=10 seconds.
3. How many seconds does the chase last?
4. How far does the rescuer travel while chasing the criminal?
5. Compare your answers to those given in the paper Pursuit Curves by Michael Lloyd, Ph.D.. Read the first paragraph in the section on the special case of pursuing a straight line target to get the definitions. In particular, k is the ratio of the fox's speed to the rabbit's speed. Then skip to the solution is given at the top of page 6 and the paragraph that follows (the paragraph incorrectly states k>1 means the rabbit is faster than the fox  -- it should be the fox is faster than the rabbit).

## Notes

• Add your names at the top of the document under the title.
• Include instructions with each of the problems; don't just create a graph or describe the graph.
• Include an answer key at the end of the document for questions 1-3. Question 4 will be answered in the main part of the document.

## Submitting the Assignment

Once you are done with the assignment, share it with the instructor. Only one person per group needs to submit the assignment, just make sure your names are all in the document itself.

1. Click the blue "Share" button in Google Docs
2. In the "Invite People" box, put in james@richland.edu
3. Change the permissions from "Can edit" to "Can comment"
4. Leave the box checked to notify people via email (This is important or I won't know that you've turned it in).
5. Click on the "Add message" box and let me know what you're sending and the names of the people in your group.
6. Click "Send"