# Math 121 - Exam 3 Study Guide

1. Sketch the graph of the derivative of the function whose graph is shown. Look at problems 3.2.25-26.
2. Find the derivative of algebraic functions that do not require the use of the chain rule. You need to know the power, product, and quotient rules. Four parts. You may need to multiply or divide before differentiating. Look at problems 3.3.1-20
3. Match the graphs of the functions with the graphs of their derivatives. Eight parts. Look at problem 3.2.23
4. The values of x, f, f', g, and g' are given in a table. Use the rules of derivatives to find the derivatives as the specified point. Five parts. Look at problems 3.4.19-22; 3.6.5-6, 71
5. Find a higher order derivative. Look at problems 3.3.37-40
6. Find f'(x) for trigonometric functions. Two parts. Look at problems 3.5.1-18
7. Find f'(x) using the chain rule. Three parts. May involve trigonometric functions. Look at problems 3.6.7-40
8. Find the differential dy. Look at problems 3.9.37-40.
9. Use a local linear approximation to estimate the value given. Look at problems 3.9.19-27.
10. Use implicit differentiation to find dy/dx. Look at problems 3.7.11-20
11. Related rate problem. Look at problems 3.8.10-47
12. Use the limit definition of a derivative to find the derivative. Look at problems 3.2.9-14 (only the part about finding the derivative) or 3.2.15-20.
13. For the accompanying graph, find the average rate of change over an interval and the instantaneous rate of change at a specific time. Look at problem 3.1.1-4, 17-19.

## Notes

• Most problems are similar to those from the textbook.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 Total 5 12 16 15 4 6 12 3 5 5 5 6 6 100