# Math 121: Chapter 2 Exam Study Guide

1. Use the graph of y = f(x) to estimate the average rate of change over an interval, the instantaneous rate of change at a point, and the equation of the tangent line at a point.
2. The graph of y = f'(x) is given. Note: This is the derivative, not the function itself. Identify the points where the derivative is increasing and decreasing most rapidly, the points where the original function is increasing and decreasing most rapidly, where the original function has a horizontal tangent, and where there is a relative maximum or minimum in the original function.
3. Differentiate. These involve the basic functions, the trignometric functions, and the chain rule. You do not need the product or quotient rule for any of these. Eight parts.
4. Find the second derivative. Two parts.
5. Find and simplify the derivative. These involve the product and quotient rules.
6. Find the derivative implicitly.
7. Related rate problem.
8. Find the derivative using the limit definition. You will need to have the limit definition memorized.
9. Find the equation of the line tangent to the given function at the indicated point.
10. Find the derivative. These could be from anywhere in the chapter. Four 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.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 10 12 24 8 10 5 5 5 5 16 100