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CHAPTER 3

The Derivative SECTION 3.1 1. Find the average rate of change of y with respect to x over the interval [1, 5]. y = f (x) = A. 0.48

B. −0.48

C. 0.96

2 x2

D. −0.96

2. Find the average rate of change of y with respect to x over the interval [1, 4]. y = f (x) = x5 A. 256

B. −256

C. 341

D. −341

3. Find the instantaneous rate of change of y = 3x2 with respect to x at x0 = 3. A. 27

B. 18

4. Find the instantaneous rate of y =

C. 12 1 with respect to x at x0 = 5. x

B. −1

A. 1

D. 9

C. −0.25

D. −0.04

5. Find the instantaneous rate of y = 4x5 with respect to x at a general point x0 . A. 20x40

B. 4x40

C. 16x40

D. 5x0

8 with respect to x at a general point x0 . x 3x0 8 2 B. − D. − 2 C. − 2 8 x0 x0

6. Find the instantaneous rate of y = A. −

2 x0

7. Find the slope of the tangent to the graph of f (x) = x3 − 2 at a general point x0 . A. 3x0 − 2

B. 3x20 − 2

C. 3x20

D. 3x0

8. Answer true or false. The slope of the tangent line to the graph of f (x) = x3 − 5 at x0 = 3 is 22. 9. Answer true or false. Use a graphing utility to graph y = 3x2 on [0, 5]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is increasing over the graphed domain. 10. Use a graphing utility to graph y = x2 − 8x + 1 on [0, 10]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is zero at what time? Assume time is in seconds. A. 0 s

C. −1 s

B. 1 s

D. 4 s

11. A rock is dropped from a height of 16 feet and falls toward earth in a straight line. In t s the rock drops a distance of 16t2 feet. What is the instantaneous velocity downward when it hits the ground? A. 4 ft/s

B. 3 ft/s

C. 2 ft/s

D. 1 ft/s

12. Answer true or false. The magnitude of the instantaneous velocity is always less than the magnitude of the average velocity. 13. Answer true or false. If a rock is thrown straight upward from the ground, when it returns to earth its average velocity will be its initial velocity. 1


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