Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the open intervals on which the graph of  is concave
downward or concave upward.
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2.
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Determine the open intervals on which the graph of  is concave
downward or concave upward.
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3.
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Determine the open intervals on which the graph of the function 
is concave upward or concave downward.
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4.
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Determine the open intervals on which the graph of  is concave
downward or concave upward.
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5.
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Find all points of inflection on the graph of the function  .
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6.
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Find the points of inflection and discuss the concavity of the
function. 
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7.
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Find the points of inflection and discuss the concavity of the function  . a. | no inflection points; concave up on  | b. | no inflection
points; concave down on  | c. | inflection point at
x = 16; concave up on  | d. | inflection point at
x = 0; concave up on  ; concave down on  | e. | inflection point at x = 16; concave down on  |
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8.
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Find all points of inflection, if any exist, of the graph of the function  . Round your answers to two decimal places. a. | 
| b. |  | c. |  | d. |  | e. | no points of
inflection |
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9.
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Find the point of inflection of the graph of the function 
on the interval  .
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10.
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Find the points of inflection and discuss the concavity of the function  on the interval  .
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11.
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Find the points of inflection and discuss the
concavity of the function  on the interval
 .
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12.
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Find all relative extrema of the function  . Use the
Second Derivative Test where applicable. a. | relative max:  ; no relative min | b. | no relative max; no
relative min | c. | relative min:  ; relative max: 
| d. | relative min:  ; no relative max | e. | relative min:  ; relative max:  |
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13.
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Find all relative extrema of the function  . Use the
Second Derivative Test where applicable. a. | relative max:  ; no relative min | b. | relative min:  ; no relative max | c. | relative min:  ; no relative
max | d. | relative max:  ; no relative min | e. | no relative max or
min |
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14.
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Find all relative extrema of the function  . Use the
Second Derivative Test where applicable. a. | relative minimum:  | b. | relative minimum:
 | c. | relative maximum:
 | d. | relative minimum:
 | e. | relative maximum:
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15.
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Find all relative extrema of the function  . Use the
Second Derivative Test where applicable. a. | relative max: (1, –2); no relative min | b. | no relative max or
min | c. | relative min: (0, –3); no relative max | d. | relative max: (1,
–2); relative min: (0, –3) | e. | relative max: (0, –3); no relative
min |
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16.
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The graph of f is shown. Graph f, f' and
f'' on the same set of coordinate axes.
 a. |  | d. |  | b. |  | e. | none of the above | c. |  |
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17.
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Find the cubic function of the form  where 
and the coefficients  are real numbers, which satisfies the
conditions given below. Relative maximum:  Relative minimum:  Inflection point: 
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18.
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Suppose a manufacturer has determined that the total cost C of operating
a factory is  where x is the number of units
produced. At what level of production will the average cost per unit be minimized? (The average cost
per unit is C/ x.)
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19.
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Suppose the annual sales S of a new product is given by 
where t is time in years. Find the exact time when the annual sales are increasing at the
greatest rate. Round your answer to three decimal places.
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