**Problems 1-4**

Follow the steps in Example 1 for the distances given in Table 18.1.
Problems 5-8

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.
Problems 9-12

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.
Problems 13-17

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.
Problem 18

This problem is designed to develop your sense of what is meant by average rate of change. Look at the sequence of numbers in Problems 13-17. For this problem, draw a tangent line and estimate the slope.
Problems 19-25

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.
Problem 26

This problem is designed to develop your sense of what is meant by average rate of change. Look at the sequence of numbers in Problems 19-25. For this problem, draw a tangent line and estimate the slope.
Problems 27-32

These problems were designed to test your intuitive notion of a tangent line. Try tracing the giving curve on your own paper before drawing the tangent line. See Figure 18.16.
Problems 33-36

See Example 2 (average rate of change) and Example 4 (instantaneous rate of change).
Problems 37-38

There are five steps (as shown in Examples 4 and 5). Work this problem in small steps as shown in Example 5. Begin with by writing down the part in Example 5 that is in boldface, and then go on for the given function.
Problems 39-40

Use the formula for the derivative of e
Problems 41-42

There are five steps (as shown in Examples 4 and 5). Work this problem in small steps as shown in Example 5. Begin with by writing down the part in Example 5 that is in boldface, and then go on for the given function. See Example 5.
Problems 43-46

Remember that the equation of a line with slope
Problems 47-56

These are complicated problems with many steps in the solution. Carefully study Example 8, and follow the steps shown there.
### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.

There are many sources for homework help on the internet.

Algebra.help

Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.

http://www.algebrahelp.com/

Ask Dr. Math

Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.

http://mathforum.org/dr.math/

Quick Math

This site provides online graphing calculators. This is especially useful if you do not have your own calculator.

http://www.quickmath.com/

The Math Forum @ Drexel

This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the linksĀ in the right-hand column.

http://mathforum.org/

Follow the steps in Example 1 for the distances given in Table 18.1.

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.

This problem is designed to develop your sense of what is meant by average rate of change. Look at the sequence of numbers in Problems 13-17. For this problem, draw a tangent line and estimate the slope.

These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.

This problem is designed to develop your sense of what is meant by average rate of change. Look at the sequence of numbers in Problems 19-25. For this problem, draw a tangent line and estimate the slope.

These problems were designed to test your intuitive notion of a tangent line. Try tracing the giving curve on your own paper before drawing the tangent line. See Figure 18.16.

See Example 2 (average rate of change) and Example 4 (instantaneous rate of change).

There are five steps (as shown in Examples 4 and 5). Work this problem in small steps as shown in Example 5. Begin with by writing down the part in Example 5 that is in boldface, and then go on for the given function.

Use the formula for the derivative of e

^{x}. See Example 6.

There are five steps (as shown in Examples 4 and 5). Work this problem in small steps as shown in Example 5. Begin with by writing down the part in Example 5 that is in boldface, and then go on for the given function. See Example 5.

Remember that the equation of a line with slope

*m*passing through the point (

*s, t*) is

*y – s = m(x – t)*. The number

*m*is the value of the derivative of the function at for the given

*x*-value. See Example 7.

These are complicated problems with many steps in the solution. Carefully study Example 8, and follow the steps shown there.