Larson_Calculus_10e ch03sec02
MULTIPLE CHOICE
1. 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
2. Determine whether Rolle’s Theorem can be applied to the function on the closed
interval [–1,3]. If Rolle’s Theorem can be applied, find all values of c in the open interval (–1,3) such
that
a.
Rolle’s Theorem applies; c = 1
b.
Rolle’s Theorem applies; c = 2
c.
Rolle’s Theorem applies; c = 0
d.
Rolle’s Theorem applies; c = –1
e.
Rolle’s Theorem does not apply
3. 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
4. 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
5. 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
6. 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; c = 0
b.
Rolle’s Theorem applies;
c.
Rolle’s Theorem applies;
d.
Rolle’s Theorem applies;
e.
Rolle’s Theorem does not apply.
7. 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
8. 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 .
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
9. 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
10. 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
11. The height of an object t seconds after it is dropped from a height of 250 meters is
Find the time during the first 8 seconds of fall at which the instantaneous velocity
equals the average velocity.
a.
32 seconds
b.
19.6 seconds
c.
6.38 seconds
d.
4 seconds
e.
2.45 seconds
12. 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.
a.
b.
c.
d.
e.
13. 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. During what month does equal
the average value of during the first year?
a.
October
b.
July
c.
December
d.
April
e.
March
14. 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.
15. Which of the following functions passes through the point and satisfies ?
a.
b.
c.
d.
e.
16. Find a function f that has derivative and with graph passing through the point (5,6).
a.
b.
c.
d.
e.