## MAT123 Fall 2006     Review for Final Exam

Note:   This exam will be cumulative in multiple choice format. There are 45 questions each worth 4 points, with 4 possible answers.
You may use a graphing calculator, however, you must follow the instructions on our Course Description page as to which models are admissable. We will strictly enforce those rules. The calculators permitted may not be of use for all questions on the exam, notably when a problem asks for an exact answer. Make sure you have good batteries, you know how to set modes and appropriate window sizes, and you can plot and interpret simple graphs.

Recommended preparation for the Final:

Revisit the Feview Guide for Midterm I
You may want to log into the Grade Report and work through the solutions of the First Midterm again, which are posted there.

Revisit the Review Guide for Midterm II
You may want to log into the Grade Report and work through the solutions of the Second Midterm again, which are posted there.

Topics for review from Chapters 5 and 6 can be found on pp622-626 and pp702-708 of the main text.

Summary: Definitions and Concepts, including Examples

```5.2   a - c,  all                    6.1   a - c,  all
5.3   a - d,  all                    6.2   d - e
5.5   a - c,  all
```

Review Exercises (pp623-625 and p705):

```5.2   15 20 29                       6.1    1  7 11
5.3   33 35 41                       6.2   13 17 21
5.5   51 56 61
```

In addition, you should carefully review all assigned homework problems, both even- and odd-numbered. You might also want to look at the relevant portions of the Chapter 5 and 6 Tests, pp372-374 and pp707-708.

When reviewing the material of the Calculus Supplement, focus on the basic understanding of the concepts and the simplest applications: Make sure you know how to compute the average rate of change of a function y=f(x) on an interval [a,b], and how to find the instantaneous rate of change or the derivative f'(x)of f at a point x more and more accurately, by considering the average change on smaller and smaller intervals about x. Be familiar with this process for the three ways by which a function can be given: table, graph, and formula. Make sure you understand the equivalent graphic approach, where the average rate of change is the slope of a secant, the instantaneous rate f'(x) the slope of the tangent at x of the graph of f. You should be able to plot the graph of the derivative function f' into a plot of the graph of f. Main topics to work on: Interpretation of f'>0 and f'<0 on some interval; local linear approximation; using the Delta notation for differences; interpretation of the second derivative: f">0 means concave up, f"<0 concave down; marginal cost and revenue. It may be conceptually very helpful in this general context to always think first of a motion, when x=t is the time and y=s=f(t) the position of an object moving along a straight line. Then y'=s'=ds/dt= v(t) is the instantaneous velocity, y"=s"=v'=dv/dt=a(t) the acceleration.

Carefully review all assigned homework problems from the Supplement, both even- and odd-numbered.

Make sure you check for further announcements and instructions for this exam regularly.

December 8, 2006