The Nature of Mathematics, 12th Edition
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Chapter 18
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Section 18.3 Homework Hints

    Problems 1-2
    These problems are designed to develop your sense of what is meant by average rate of change. See Example 3; for part d, draw a tangent line and estimate the slope.
    Problem 3
    Review the meaning of average and then use it to answer the question as shown in  Example 1.
    Problems 4-5
    The average is found by evaluating f (x + h) - f (x) divided by h, where h is the duration of the time period. See Example 3.
    Problems 6-11
    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 12-15
    See Example 2 (average rate of change) and Example 4 (instantaneous rate of change).
    Problems 16-17
    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 18-19
    Use the formula for the derivative of ex. See Example 6.
    Problems 20-21
    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 22-25
    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.
    Problems 26-29
    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 links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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