Math 1854, Homework on Chapter 2

Please re-read the Homework Guidelines on page 4 of the syllabus and ask questions about any part that you don't understand. I will count off more on the Chapter 2 and later homework for not following the guidelines than I count off on Chapter 1. If there are some of the parts that you don't think are necessary, please do come and talk with me about them outside of class.

2.1 3, 4, 5, 7, 9, 11

2.2 5, 8, 9, 11, 13, 15, 16, 23

2.3 3, 5, 8, 9, 13, 15, 17, 23, 29, 35

2.4 1, 4, 9

2.4 11, 13, 16, 17

2.5 1, 2, 3, 5, 9, 11

2.6 3, 5, 7, 9

2.7 1, 3, 7, 9, 10

2.8 3, 4, 5

To review for Test 2:

• Read the following list of topics and make sure you can work typical problems on each topic.
• Go over all homework and do the chapter review. Many of the test questions will look very similar to some problem in the homework.
• Remember that this test will also include some problems from Chapter 1. Be sure that you fully understand everything on that test and the assigned problems in the Precalculus Review and the Chapter Review.

1. Velocity as related to distance. Average velocity and instantaneous velocity.

2. Rate of change of a function. Average rate of change and instantaneous rate of change. The derivative at a point as the instantaneous rate of change. Graphical interpretation of each (slope of a line between two points and slope of the tangent line).

3. Estimating the derivative at a point graphically, numerically, and finding it algebraically (as long as the algebra doesn't get too hard!). Also, understanding which is which, so that you can do each problem by the method requested.

4. Generalizing to the derivative function. Graphing a derivative function from a graph of the function. The derivative and how it relates to whether the function is increasing or decreasing.

5. Interpretation of the derivative as a rate of change. Keeping track of the units. Acceleration. Different types of notation for the derivative.

6. The second derivative as the rate of change of the first derivative. Concavity.

7. Writing the equation of the tangent line to the graph at a point (which involves finding the value of the derivative. Recall number 3 here!). Using that tangent line to estimate a function value. Is this an overestimate or underestimate?

8. For a given function (graph), tell where it is continuous or not and where it is differentiable or not. Use limit notation and one-sided limit notation.

Chapter 2 Review: (These won't be graded, but you may find them useful.)

1, 2, all of 8-14 (and compare your answers with those of other students), 15, 16, 17, 18, 19 (you don't have to graph it all that carefully to get an estimate of the slope that is accurate enough for this problem), 21

Last updated February 5, 1998. mparker@austincc.edu