Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Use the graph of the function  given below to
estimate the open intervals on which the function is increasing or decreasing. 
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2.
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Identify the open intervals where the function  is
increasing or decreasing.
a. | decreasing on  | b. | increasing on  | c. |  | d. | decreasing on  ; increasing on  | e. |  |
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3.
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Identify the open intervals where the function  is
increasing or decreasing.
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4.
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Identify the open intervals on which the function  is
increasing or decreasing.
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5.
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Find the critical number of the function  .
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6.
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Find the open interval(s) on which  is increasing or
decreasing.
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7.
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Find the relative extremum of  by applying the First
Derivative Test. a. | relative minimum:  | b. | relative maximum:
 | c. | relative minimum:
 | d. | relative minimum:
 | e. | relative maximum:
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8.
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For the function  : (a) Find the critical numbers
of f (if any); (b) Find the open intervals where the function is increasing or
decreasing; and (c) Apply the First Derivative Test to identify all relative
extrema. Then use a graphing utility to confirm your results.
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9.
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For the function  : (a) Find the critical numbers
of f (if any); (b) Find the open intervals where the function is increasing or
decreasing; and (c) Apply the First Derivative Test to identify all relative
extrema. Use a graphing utility to confirm your results.
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10.
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Find the open interval(s) on which the function  is
increasing in the interval  Round numerical values in your answer to
three decimal places.
a. | increasing on:  | b. | increasing on:  | c. | increasing on:  | d. | increasing on:  | e. | increasing on:  |
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11.
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Find the relative maxima of  on the interval  by applying the First Derivative Test. Round numerical values in your answer to three
decimal places. a. | relative maxima:  | b. | relative maxima:
 | c. | relative maxima:
 | d. | relative maxima:
 | e. | relative maxima:
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12.
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Find the relative minima of  on the interval  by applying the First Derivative Test. Round numerical values in your answer to three
decimal places. a. | relative minima:  | b. | relative minima:
 | c. | relative minima:
 | d. | relative minima:
 | e. | relative minima:
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13.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f.  a. |  | d. |  | b. |  | e. | The derivative of f does not
exist. | c. |  |
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14.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f.
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15.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f.
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16.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f. 
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17.
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A ball bearing is placed on an inclined plane and
begins to roll. The angle of elevation of the plane is  radians. The distance (in
meters) the ball bearing rolls in t seconds is  . Determine the speed of the ball bearing after t
seconds.
a. | speed:  meters per
second | b. | speed:  meters per
second | c. | speed:  meters per
second | d. | speed:  meters per
second | e. | speed:  meters per
second |
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18.
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A ball bearing is placed on an inclined
plane and begins to roll. The angle of elevation of the plane is  radians. The
distance (in meters) the ball bearing rolls in t seconds is  . Determine
the value of  after one second. Round numerical values in
your answer to one decimal place.
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