# 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. The graph of a function is shown. Illustrate the mean value theorem on the specified interval and then find the values of x that are guaranteed by the mean value theorem.
3. Find the differential.
4. 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. Give the values where there are horizontal tangents and inflection points.
5. Find the limits. Some problems are indicated with a *; show work on these for full credit. Eight parts (3 that need work shown).
6. Use Newton's method to approximate the zeros by finding the next four terms in the sequence. The initial seeds are given to you.
7. Use differentials and a local linear approximation to approximate the value of a function at a specific point.
8. 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. Six parts.
9. Applied maximization or minimization problem. The primary equation is given to you.
10. Applied maximization or minimization problem. You need to come up with the primary equation, but geometric formulas that you will need are given.
11. Applied maximization or minimization problem. You will need to know the distance formula.
12. 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. Some of the problems are directly from 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.
• There are two parts to the exam.
• Part 1 is questions 1-8, which must be worked without the computer and then turned in before you get part 2.
• Part 2 is questions 9-12. You should use Maxima on this part, otherwise you won't get it done in the allowed time. Problems don't particularly have nice answers, so you should given them in decimal form. Problems are similiar to those in the book, but were designed to be worked using technology. There is no work that you're going to show (it's all on Maxima) for this portion, so the responses you write on the exam will essentially be right or wrong.
• Although there are 108 possible points on the exam, the maximum grade anyone can receive is 100 points. This makes some allowance for the inability to obtain partial credit on the second part.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 9 6 4 15 24 8 5 12 5 5 5 10 108