Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the derivative of the algebraic function  .
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2.
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Use the Product Rule to differentiate  .
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3.
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Use the Product Rule to differentiate  .
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4.
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Use the Product Rule to differentiate. 
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5.
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Use the Product Rule to differentiate  .
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6.
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Use the Quotient Rule to differentiate the function
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7.
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Use the Quotient Rule to differentiate the function
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8.
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Use the Quotient Rule to differentiate the function  .
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9.
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Use the Quotient Rule to differentiate the following function 
and evaluate  .
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10.
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Find the derivative of the algebraic function  .
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11.
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Find the derivative of the function  .
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12.
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Find the derivative of the function.  .
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13.
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Find the derivative of the trigonometric function  .
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14.
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Find the derivative of the function.
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15.
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Find an equation of the tangent line to the graph of f at the given
point. 
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16.
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Determine all values of x, (if any), at which the graph of the function
has a horizontal tangent.  a. |  | b. |  | c. |  | d. |  | e. | The graph has no horizontal tangents. |
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17.
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The length of a rectangle is  and its height is  , where t is time in seconds and the dimensions are in inches. Find the rate of
change of the area, A, with respect to time. a. |  square inches/second | b. | 
square inches/second | c. |  square
inches/second | d. |  square inches/second | e. | 
square inches/second |
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18.
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The radius of a right circular cylinder is  and its
height is  , where t is time in seconds and the
dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with
respect to time. a. |  cubic inches per second | b. | 
cubic inches per second | c. |  cubic inches per
second | d. |  cubic inches per second | e. | 
cubic inches per second |
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19.
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The ordering and transportation cost C for the components used in
manufacturing a product is  where C is measured in thousands of
dollars and x is the order size in hundreds. Find the rate of change of C with respect
to x for x = 24. Round your answer to two decimal places. a. | –6.44 thousand dollars per hundred | b. | 8.04 thousand
dollars per hundred | c. | 3.28 thousand dollars per
hundred | d. | –4.92 thousand dollars per hundred | e. | –7.96 thousand
dollars per hundred |
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20.
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A population of 620 bacteria is introduced into a culture and grows in number
according to the equation  where t is measured in hours. Find the
rate at which the population is growing when t = 2. Round your answer to two decimal
places. a. | 226.7 bacteria per hour | b. | 68.89 bacteria per hour | c. | 65.26 bacteria per
hour | d. | 51.52 bacteria per hour | e. | 61.23 bacteria per
hour |
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21.
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When satellites observe Earth, they can scan only part of Earth's surface.
Some satellites have sensors that can measure the angle  shown in the figure. Let
h represent the satellite's distance from Earth's surface and let r represent
Earth's radius. Find the rate at which h is changing with respect to 
when  (Assume r = 4460 miles.) Round your
answer to the nearest unit.  a. | –2973 mi/radian | b. | –5150 mi/radian | c. | 5150
mi/radian | d. | –8920 mi/radian | e. | 2973 mi/radian |
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22.
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Find the second derivative of the function  .
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23.
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Find the second derivative of the function  .
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24.
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Find the second derivative of the function  .
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25.
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Given the derivative below find the requested higher-order
derivative.  .
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26.
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Suppose that an automobile's velocity starting from rest is 
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer
to one decimal place. a. | 1.9 ft/sec2 | b. | 0.9 ft/sec2 | c. | 0.6
ft/sec2 | d. | 0.2 ft/sec2 | e. | 8.3
ft/sec2 |
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