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92 Chapter 2: Differentiation
2.2 Basic Differentiation Rules and Rates of Change
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 2. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 3. Use the rules of differentiation to find the derivative of the function .
a.
b.
c.
d.
e.
____ 4. Find the derivative of the function .
a.
b.
2.2 Basic Differentiation Rules and Rates of Change 93
c.
d.
e.
____ 5. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 6. Use the rules of differentiation to find the derivative of the function .
a.
b.
c.
d.
e.
____ 7. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 8. Find the slope of the graph of the function at the given value.
when
a.
b.
c.
d.
e.
94 Chapter 2: Differentiation
____ 9. Find the slope of the graph of the function at the given value.
when
a.
b.
c.
d.
e.
____ 10. Find the slope of the graph of the function at the given value.
when
a.
b.
c.
d.
e.
____ 11. Find the slope of the graph of the function at .
a.
b.
c.
d.
e.
2.2 Basic Differentiation Rules and Rates of Change 95
____ 12. Find the slope of the graph of the function at the given value.
at
a.
b.
c.
d.
e.
____ 13. Find the slope of the graph of the function at .
a.
b.
c.
d.
e.
____ 14. Find the slope of the graph of the function at the given value.
at
a.
b.
c.
d.
e.
____ 15. Find the derivative of the function .
a.
b.
c.
d.
e.
96 Chapter 2: Differentiation
____ 16. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 17. Determine all values of , (if any), at which the graph of the function has a horizontal
tangent.
a.
b.
c.
d.
e. The graph has no horizontal tangents.
____ 18. Determine all values of , (if any), at which the graph of the function has a horizontal
tangent.
a.
b.
c.
d.
e. The graph has no horizontal tangents.
____ 19. Determine all values of , (if any), at which the graph of the function has a horizontal
tangent.
a.
b.
c.
d.
e. The graph has no horizontal tangents.
2.2 Basic Differentiation Rules and Rates of Change 97
____ 20. Suppose the position function for a free-falling object on a certain planet is given by
. A silver coin is dropped from the top of a building that is 1370 feet tall.
Determine the velocity function for the coin.
a.
b.
c.
d.
e.
____ 21. Suppose the position function for a free-falling object on a certain planet is given by
. A silver coin is dropped from the top of a building that is 1372 feet tall.
Determine the average velocity of the coin over the time interval .
a. –113 ft/sec
b. 80 ft/sec
c. 112 ft/sec
d. –112 ft/sec
e. –80 ft/sec
____ 22. Suppose the position function for a free-falling object on a certain planet is given by
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find
the instantaneous velocity of the coin when .
a. –96 ft/sec
b. –32 ft/sec
c. –20 ft/sec
d. –144 ft/sec
e. –48 ft/sec
____ 23. Suppose the position function for a free-falling object on a certain planet is given by
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find
the time required for the coin to reach ground level. Round your answer to the three decimal places.
a. 2.849 sec
b. 10.273 sec
c. 10.693 sec
d. 3.087 sec
e. 10.091 sec
98 Chapter 2: Differentiation
____ 24. Suppose the position function for a free-falling object on a certain planet is given by
. A silver coin is dropped from the top of a building that is 1370 feet tall. Find
velocity of the coin at impact. Round your answer to the three decimal places.
a. –286.705 ft/sec
b. –138.492 ft/sec
c. –111.041 ft/sec
d. –276.984 ft/sec
e. –261.984 ft/sec
____ 25. A ball is thrown straight down from the top of a 300-ft building with an initial
velocity of –12 ft per second. The position function is . What is the velocity of
the ball after 4 seconds?
a. The velocity after 4 seconds is –76 ft per second.
b. The velocity after 4 seconds is –116 ft per second.
c. The velocity after 4 seconds is –140 ft per second.
d. The velocity after 4 seconds is –52 ft per second.
e. The velocity after 4 seconds is –280 ft per second.
____ 26. A projectile is shot upwards from the surface of the earth with an initial velocity of
108 meters per second. The position function is .
What is its velocity after 7 seconds?
a. The velocity after 7 seconds is 181.7 meters per second.
b. The velocity after 7 seconds is –142.3 meters per second.
c. The velocity after 7 seconds is 39.4 meters per second.
d. The velocity after 7 seconds is 73.7 meters per second.
e. The velocity after 7 seconds is –176.6 meters per second.
____ 27. The volume of a cube with sides of length s is given by . Find the rate of
change of volume with respect to when centimeters.
a. 648 cm2
b. 216 cm2
c. 36 cm2
d. 108 cm2
e. 72 cm2
2.2 Basic Differentiation Rules and Rates of Change 99
2.2 Basic Differentiation Rules and Rates of Change
Answer Section
100 Chapter 2: Differentiation
