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. Look at problem 3.1.10.
2. Match the graphs of the functions with the graphs of their derivatives. Five parts. Look at problem 3.2.23.
3. Sketch the graph of the derivative of the function whose graph is shown. Look at problems 3.2.25-26
4. Find the derivative. Four parts. Look at problems 3.3.1-28.
5. Find f'(x) for trigonometric functions. Four parts. Look at problems 3.4.1-18.
6. Find f'(x) using the chain rule. Four parts. Look at problems 3.5.1-39.
7. Find the derivatives as the specified point. Six parts. Look at supplementary exercise 3.10.
8. Find the differential dy. Look at problems 3.6.9-12.
9. Use the limit definition of the derivative (Definition 3.2.2) to find the derivative of the given function. Look at problems 3.2.9-14. Note: 9-14 ask for the equation of the tangent line, I'm just asking for the derivative. 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.
10. Use a local linear approximation to estimate the value given. Look at problems 3.6.27-35.
11. Find a higher order derivative. Look at problems 3.3.41-44.
12. True / false statements regarding continuity and differentiability of functions. Two parts.
13. Write formulas for the slope of a secant line and the slope of a tangent line. Two parts.

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