Larson_Calculus_10e ch02sec03
MULTIPLE CHOICE
1. Find the derivative of the algebraic function .
a.
b.
c.
d.
e.
2. Use the Product Rule to differentiate .
a.
b.
c.
d.
e.
3. Use the Product Rule to differentiate .
a.
b.
c.
d.
e.
4. Use the Product Rule to differentiate.
a.
b.
c.
d.
e.
5. Use the Product Rule to differentiate .
a.
b.
c.
d.
e.
6. Use the Quotient Rule to differentiate the function .
a.
b.
c.
d.
e.
7. Use the Quotient Rule to differentiate the function .
a.
b.
c.
d.
e.
8. Use the Quotient Rule to differentiate the function .
a.
b.
c.
d.
e.
9. Use the Quotient Rule to differentiate the following function and evaluate .
a.
b.
c.
d.
e.
10. Find the derivative of the algebraic function .
a.
b.
c.
d.
e.
11. Find the derivative of the function .
a.
b.
c.
d.
e.
12. Find the derivative of the function.
.
a.
b.
c.
d.
e.
13. Find the derivative of the trigonometric function .
a.
b.
c.
d.
e.
14. Find the derivative of the function.
a.
b.
c.
d.
e.
15. Find an equation of the tangent line to the graph of f at the given point.
a.
b.
c.
d.
e.
16. 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.
17. 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
18. 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
19. 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
20. 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
21. 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
22. Find the second derivative of the function .
a.
b.
c.
d.
e.
23. Find the second derivative of the function .
a.
b.
c.
d.
e.
24. Find the second derivative of the function .
a.
b.
c.
d.
e.
25. Given the derivative below find the requested higher-order derivative.
.
a.
b.
c.
d.
e.
26. 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