Math 121 - Chapter 3 Study Guide

1. For the accompanying position versus time graph, find the average velocity over an interval, the places where the instantaneous velocity is zero, the times at which the instantaneous velocity is a maximum or minimum, and the instantaneous velocity at a specific time.
2. Sketch the graph of the derivative of the function whose graph is shown.
3. Match the graphs of the functions with the graphs of their derivatives. Five parts.
4. Find the differential dy.
5. Use a local linear approximation to estimate the value given.
6. 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.
7. Find f'(x) for trigonometric functions. Three parts.
8. Find f'(x) using the chain rule. Five parts.
9. The values of f, f ', g, and g' are given in a table. Use the rules of derivatives to find the derivatives as the specified point. Six parts.
10. Use the limit definition of the derivative to find the derivative of the given function. Also note that this is a problem where I will be grading work more than the answer. Be sure you write the limit in every time until you actually take the limit.
11. Find a higher order derivative.
12. Use implicit differentiation to find dy/dx.

Notes: