# 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. The graph of a function is given. Sketch the derivative of the function using the same coordinate system. Three parts.
4. Related rate story problem. Very similar to questions from the book. Two parts.
5. Find the derivative using the limit definition. You will need to have the limit definition memorized.
6. Differentiate. These come from throughout the chapter. You will need to know the basic functions, trigonometric functions, product, quotient, and chain rules. Ten parts.
7. Find the second derivative. Two parts.
8. Find the derivative using implicit differentiation.
9. Find the equation of the line tangent to the given function at the indicated point.
10. Find the derivative. These are some more advanced problems. Three 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.
• Concentrate on the problems that are worth the most points.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 6 10 9 10 5 30 6 6 6 12 100