# Math 121: Chapter 3 Exam Study Guide

1. Look at a graph of the function and identify places where f' and f'' are zero or undefined. Make a sign chart for f' and f''. Give coordinates of any extrema or inflection points.
2. You have a continuous function with exactly one critical point. Information is given and you should decide whether the point is a relative maximum, relative minimum, neither, or it is impossible to tell from the information given. You should know the first and second derivative tests for this. Ten parts.
3. A function and its first two derivatives are given in factored form. Use them to make a sign chart for f, f', and f''. Know the meaning of the signs for each of the sign charts. Note: By "know the meaning", I mean be able to describe how to find the answer rather than actually finding the answer. Give the values where there are horizontal tangents and inflection points.
4. Find the limits. Some problems are indicated with a *; show work on these for full credit. Eight parts (3 that need work shown).
5. Use Newton's method to approximate the zeros by finding the next three terms in the sequence as well as the final value. The initial seeds are given to you.
6. Use differentials and a local linear approximation to approximate the value of a function at a specific point.
7. Applied maximization or minimization problem. The primary equation is given to you.
8. Applied maximization or minimization problem. You need to come up with the primary equation, but geometric formulas that you will need are given.
9. Applied maximization or minimization problem. You will need to know the distance formula.
10. Find the x coordinate of all relative extrema and points of inflection. Two parts.

## Notes

• Most of the problems are similar to those in the textbook.
• Don't spend too long on any one problem. If you get stuck, make a note to come back and then move on.
• Part 1 of the exam consists of questions 1-6, which must be worked without the computer and then turned in before you get part 2.
• Part 2 of the exam consists of questions 7-10. You should use Maxima on this part, otherwise you won't get it done in the allowed time. The problems have probably have nasty answers, so you should give them in decimal form.Problems are similiar to those in the book, but were designed to be worked using technology. Since this is done using technology, if you want any partial credit, either write down some of the key equations on the paper or email the Maxima file to the instructor after the exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 9 10 18 24 8 5 6 6 6 8 100