Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine whether Rolle's Theorem can be applied to 
on the closed interval  If Rolle's Theorem can be applied, find
all values of c in the open interval  such that  a. | Rolle's Theorem applies; c = 6, c = 5 | b. | Rolle's Theorem
applies; c = 4, c = 6 | c. | Rolle's Theorem applies; c =
5 | d. | Rolle's Theorem applies; c = 4 | e. | Rolle's Theorem
does not apply |
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2.
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Determine whether Rolle's Theorem can be applied to the function  on the closed interval  If Rolle's Theorem can be applied, find
all numbers c in the open interval  such that  a. | Rolle's Theorem applies;  | b. | Rolle's Theorem
applies;  | c. | Rolle's Theorem
does apply;  | d. | Rolle's Theorem
applies;  | e. | Rolle's Theorem
does not apply |
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3.
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Determine whether Rolle's Theorem can be applied to the function  on the closed interval  . If Rolle's Theorem can be applied, find
all numbers c in the open interval  such that  . a. | Rolle's Theorem applies;  | b. | Rolle's Theorem
applies;  | c. | Rolle's Theorem
applies;  | d. | Rolle's Theorem
applies;  | e. | Rolle's Theorem
does not apply |
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4.
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Determine whether Rolle's Theorem can be applied to 
on the closed interval  If Rolle's Theorem can be applied, find
all values of c in the open interval  such that  a. | c = 8 | b. | c = 12, c =
11 | c. | c = 11, c = 8 | d. | c = 12 | e. | Rolle's Theorem
does not apply |
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5.
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The ordering and transportation cost C for components used in a
manufacturing process is approximated by  where C is measured
in thousands of dollars and x is the order size in hundreds. According to Rolle's
Theorem, the rate of change of the cost must be 0 for some order size in the interval 
Find this order size. Round your answer to three decimal places. a. | 9.657 components | b. | 6.828 components | c. | 8.000
components | d. | 6.000 components | e. | 4.828
components |
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6.
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Determine whether the Mean Value Theorem can be
applied to the function  on the closed interval [3,9]. If the
Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that
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a. | MVT applies; c = 6 | b. | MVT applies; c = 7 | c. | MVT applies; c = 4 | d. | MVT applies; c = 5 | e. | MVT applies;
c = 8 |
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7.
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Determine whether the Mean Value Theorem can be applied to the function  on the closed interval [0,16]. If the Mean Value Theorem can be applied, find
all numbers c in the open interval (0,16) such that  . a. | MVT applies;  | b. | MVT applies;
4 | c. | MVT applies;  | d. | MVT applies;
8 | e. | MVT does not apply |
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8.
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The height of an object t seconds after it is dropped from a height of
550 meters is  Find the average velocity of the object
during the first 7 seconds. a. | 34.30 m/sec | b. | –34.30 m/sec | c. | –49.00
m/sec | d. | 49 m/sec | e. | –16.00
m/sec |
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9.
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A company introduces a new product for which the number of units sold S
is  where t is the time in months since
the product was introduced. Find the average value of  during the first
year.
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10.
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A plane begins its takeoff at 2:00 P.M. on a 2200-mile flight. After 12.5 hours,
the plane arrives at its destination. Explain why there are at least two times during the flight when
the speed of the plane is 100 miles per hour.
a. | By the Mean Value Theorem, there is a time when the speed of the plane must equal the
average speed of 303 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 303 mi/hr and
decelerating from 303 mi/hr.
| b. | By the Mean Value Theorem, there is a time when
the speed of the plane must equal the average speed of 152 mi/hr. The speed was 100 mi/hr when the
plane was accelerating to 152 mi/hr and decelerating from 152 mi/hr.
| c. | By the Mean Value
Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr. The
speed was 100 mi/hr when the plane was accelerating to 88 mi/hr and decelerating from 88
mi/hr.
| d. | By the Mean Value Theorem, there is a time when the speed of the plane must equal the
average speed of 117 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 117 mi/hr and
decelerating from 117 mi/hr.
| e. | By the Mean Value Theorem, there is a time when
the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the
plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr. |
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11.
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Which of the following functions passes through the point 
and satisfies  ?
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12.
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Find a function f that has derivative  and with
graph passing through the point (5,6).
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