# 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. 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.
4. Find the limits. Show work for full credit. Five parts.
5. Applied maximization or minimization problem. The primary equation is given to you.
6. Use Newton's method to approximate the zeros.
7. Find the differential.
8. Use differentials and a local linear approximation to approximate the value of a function at a specific point. Similar to the cube root of 27.4 problem that we did in class.
9. Given a rational function, find out everything you can about it and make a sketch. Label the key points on the graph. The rational function is given in expanded form, factored form, and results of long division. Different forms will be helpful in finding different values.

## 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.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 Total 12 8 18 20 8 7 5 8 14 100