Name: 
 

MAT 121 Applied Calculus Section 14 Test #2



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

mc001-1.jpg
a.
mc001-2.jpg
b.
mc001-3.jpg
c.
mc001-4.jpg
d.
mc001-5.jpg
 

 2. 

Let mc002-1.jpg

Find the equation of the tangent line to the curve at the point mc002-2.jpg.
a.
mc002-3.jpg
b.
mc002-4.jpg
c.
mc002-5.jpg
d.
mc002-6.jpg
 

 3. 

Let mc003-1.jpg.

Find the derivative mc003-2.jpg of mc003-3.jpg and the point on the graph of mc003-4.jpg where the tangent line to the curve is horizontal.
a.
mc003-5.jpg
b.
mc003-6.jpg
c.
mc003-7.jpg
d.
mc003-8.jpg
 

 4. 

During the construction of a high-rise building, a worker accidentally dropped his portable electric screwdriver from a height of 144 ft. After t sec, the screwdriver had fallen a distance of mc004-1.jpg ft.

What was the velocity of the screwdriver at the time it hit the ground?
a.
48 ft/sec
b.
12 ft/sec
c.
96 ft/sec
d.
768 ft/sec
 

 5. 

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function

mc005-1.jpg

Find the rate of population growth at mc005-2.jpg min.
a.
125 bacteria per minute
b.
148 bacteria per minute
c.
120 bacteria per minute
d.
113 bacteria per minute
 

 6. 

The position of car A and car B, starting out side by side and traveling along a straight road, is given by mc006-1.jpg and mc006-2.jpg, respectively, where s is measured in feet and t is measured in seconds (see the accompanying figure).

mc006-3.jpg

Which car is traveling faster at mc006-4.jpg?
a.
Car A is traveling faster at mc006-5.jpg, car A is traveling faster at mc006-6.jpg, cars are traveling at the same speed at mc006-7.jpg
b.
Car B is traveling faster at mc006-8.jpg, car A is traveling faster at mc006-9.jpg, car A is traveling faster at mc006-10.jpg
c.
Cars are traveling at the same speed at mc006-11.jpg, car A is traveling faster at mc006-12.jpg, car B is traveling faster at mc006-13.jpg
d.
Car B is traveling faster at mc006-14.jpg, cars are traveling at the same speed at mc006-15.jpg, car A is traveling faster at mc006-16.jpg
 

 7. 

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule mc007-1.jpg, where N(t) denotes the population at the end of year t.

Find the rate of growth of the turtle population when mc007-2.jpg.
a.
26 turtles/yr
b.
32 turtles/yr
c.
28 turtles/yr
d.
30 turtles/yr
e.
24 turtles/yr
 

 8. 

Let  mc008-1.jpg.

Find the values of x for which mc008-2.jpg.
a.
mc008-3.jpg
b.
mc008-4.jpg
c.
mc008-5.jpg
d.
mc008-6.jpg
e.
mc008-7.jpg
 

 9. 

Find the derivative of the function f  by using the rules of differentiation.

mc009-1.jpg
a.
mc009-2.jpg
b.
mc009-3.jpg
c.
mc009-4.jpg
d.
mc009-5.jpg
e.
mc009-6.jpg
 

 10. 

Find the slope and an equation of the tangent line to the graph of the function f at the specified point.

mc010-1.jpg
a.
mc010-2.jpg
b.
mc010-3.jpg
c.
mc010-4.jpg
d.
mc010-5.jpg
e.
mc010-6.jpg
 

 11. 

Find the derivative of the function by using the rules of differentiation.

mc011-1.jpg
a.
mc011-2.jpg
b.
mc011-3.jpg
c.
mc011-4.jpg
d.
mc011-5.jpg
 

 12. 

Find the derivative of the function by using the rules of differentiation.

mc012-1.jpg
a.
mc012-2.jpg
b.
mc012-3.jpg
c.
mc012-4.jpg
d.
mc012-5.jpg
 

 13. 

Find the derivative of the function by using the rules of differentiation.

mc013-1.jpg
a.
mc013-2.jpg
b.
mc013-3.jpg
c.
mc013-4.jpg
d.
mc013-5.jpg
 

 14. 

Find the derivative of the function by using the rules of differentiation.

mc014-1.jpg
a.
mc014-2.jpg
b.
mc014-3.jpg
c.
mc014-4.jpg
d.
mc014-5.jpg
 

 15. 

Let mc015-1.jpg. Find mc015-2.jpg.
a.
mc015-3.jpg
b.
mc015-4.jpg
c.
mc015-5.jpg
d.
mc015-6.jpg
 

 16. 

Let mc016-1.jpg

Find the point(s) on the graph of f where the tangent line is horizontal.
a.
mc016-2.jpg
b.
mc016-3.jpg
c.
mc016-4.jpg
d.
mc016-5.jpg
 

 17. 

Retail revenue each year from Internet shopping is approximated by the function
mc017-1.jpg, where mc017-2.jpg is measured in billions of dollars and t is measured in years, with mc017-3.jpg corresponding to the beginning of 1997.

How fast was the retail revenue/year from Internet shopping changing at the beginning of the year 2000?
a.
mc017-4.jpg
b.
mc017-5.jpg
c.
mc017-6.jpg
d.
mc017-7.jpg
 

 18. 

Find the derivative of the function.

mc018-1.jpg
a.
mc018-2.jpg
b.
mc018-3.jpg
c.
mc018-4.jpg
d.
mc018-5.jpg
e.
mc018-6.jpg
 

 19. 

Find the derivative of the function.

mc019-1.jpg
a.
mc019-2.jpg
b.
mc019-3.jpg
c.
mc019-4.jpg
d.
mc019-5.jpg
e.
mc019-6.jpg
 

 20. 

Find an equation of the tangent line to the graph of the function at the point mc020-1.jpg.

mc020-2.jpg
a.
mc020-3.jpg
b.
mc020-4.jpg
c.
mc020-5.jpg
d.
mc020-6.jpg
e.
mc020-7.jpg
 

 21. 

Evaluate mc021-1.jpg at the value of mc021-2.jpg.

mc021-3.jpg
a.
mc021-4.jpg
b.
mc021-5.jpg
c.
mc021-6.jpg
d.
mc021-7.jpg
e.
mc021-8.jpg
 

 22. 

Find an equation of the tangent line to the graph of the function  mc022-1.jpg at the point mc022-2.jpg.
a.
mc022-3.jpg
b.
mc022-4.jpg
c.
mc022-5.jpg
d.
mc022-6.jpg
 

 23. 

Find the derivative of the function.

mc023-1.jpg
a.
mc023-2.jpg
b.
mc023-3.jpg
c.
mc023-4.jpg
d.
mc023-5.jpg
 

 24. 

Find the derivative of the function.

mc024-1.jpg
a.
mc024-2.jpg
b.
mc024-3.jpg
c.
mc024-4.jpg
d.
mc024-5.jpg
 

 25. 

Find the derivative of the function.

mc025-1.jpg
a.
mc025-2.jpg
b.
mc025-3.jpg
c.
mc025-4.jpg
d.
mc025-5.jpg
 

 26. 

The number of viewers of a television series introduced several years ago is approximated by the function  mc026-1.jpg, where N(t) (measured in millions) denotes the number of weekly viewers of the series in the t th week. Find the rate of increase of the weekly audience at the end of week 12.
a.
0.165 million/wk
b.
2.694 million/wk
c.
0.495 million/wk
d.
8.082 million/wk
e.
16.332 million/wk
 

 27. 

Suppose mc027-1.jpg. Find mc027-2.jpg given that mc027-3.jpg,   mc027-4.jpg, mc027-5.jpgmc027-6.jpg.
a.
mc027-7.jpg
b.
mc027-8.jpg
c.
mc027-9.jpg
d.
mc027-10.jpg
e.
mc027-11.jpg
 

 28. 

Find the derivative of the function.

mc028-1.jpg
a.
mc028-2.jpg
b.
mc028-3.jpg
c.
mc028-4.jpg
d.
mc028-5.jpg
 

 29. 

Find the derivative of the function.

mc029-1.jpg
a.
mc029-2.jpg
b.
mc029-3.jpg
c.
mc029-4.jpg
d.
mc029-5.jpg
 

 30. 

Find the derivative of the function.

mc030-1.jpg
a.
mc030-2.jpg
b.
mc030-3.jpg
c.
mc030-4.jpg
d.
mc030-5.jpg
 

 31. 

Find the derivative of the function.

mc031-1.jpg
a.
mc031-2.jpg
b.
mc031-3.jpg
c.
mc031-4.jpg
d.
mc031-5.jpg
 

 32. 

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is mc032-1.jpg 
where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301st oven and the marginal cost when mc032-2.jpg?
a.
The actual cost of the 301st oven is $138.12, the marginal cost when mc032-3.jpg is $138.00
b.
The actual cost of the 301st oven is $118.12,  the marginal cost when mc032-4.jpg is $36.00
c.
The actual cost of the 301st oven is $118.12,  the marginal cost when mc032-5.jpg is $120.00
d.
The actual cost of the 301st oven is $18.12,  the marginal cost when mc032-6.jpg is $156.00
e.
The actual cost of the 301st oven is $138.12,  the marginal cost when mc032-7.jpg is $156.00
 

 33. 

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation mc033-1.jpg. The weekly total cost incurred by Pulsar for producing x sets is mc033-2.jpg dollars. Compute mc033-3.jpg, mc033-4.jpg, mc033-5.jpg.
a.
mc033-6.jpg, mc033-7.jpg, mc033-8.jpg
b.
mc033-9.jpg, mc033-10.jpg, mc033-11.jpg
c.
mc033-12.jpg, mc033-13.jpg, mc033-14.jpg
d.
mc033-15.jpg, mc033-16.jpg, mc033-17.jpg
e.
mc033-18.jpg, mc033-19.jpg, mc033-20.jpg
 

 34. 

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is
mc034-1.jpg.

What is the marginal cost when mc034-2.jpg and mc034-3.jpg?
a.
mc034-4.jpg
b.
mc034-5.jpg
c.
mc034-6.jpg
d.
mc034-7.jpg
 

 35. 

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is mc035-1.jpg, where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded.

Find the marginal revenue function mc035-2.jpg.
a.
mc035-3.jpg
b.
mc035-4.jpg
c.
mc035-5.jpg
d.
mc035-6.jpg
 

 36. 

Find the second derivative of the function.

mc036-1.jpg
a.
mc036-2.jpg
b.
mc036-3.jpg
c.
mc036-4.jpg
d.
mc036-5.jpg
e.
mc036-6.jpg
 

 37. 

Find the second derivative of the function.

mc037-1.jpg
a.
mc037-2.jpg
b.
mc037-3.jpg
c.
mc037-4.jpg
d.
mc037-5.jpg
e.
mc037-6.jpg
 

 38. 

The distance s (in feet) covered by a car after t sec is given by  mc038-1.jpg.

Find a general expression for the car's acceleration at any time tmc038-2.jpg.
a.
mc038-3.jpg
b.
mc038-4.jpg
c.
mc038-5.jpg
d.
mc038-6.jpg
e.
mc038-7.jpg
 

 39. 

Find the first and second derivatives of the function.

mc039-1.jpg
a.
mc039-2.jpg
b.
mc039-3.jpg
c.
mc039-4.jpg
d.
mc039-5.jpg
e.
mc039-6.jpg
 

 40. 

Find the first and second derivatives of the function.

mc040-1.jpg
a.
mc040-2.jpg
b.
mc040-3.jpg
c.
mc040-4.jpg
d.
mc040-5.jpg
e.
mc040-6.jpg
 

 41. 

Find the first and second derivatives of the function.

mc041-1.jpg
a.
mc041-2.jpg
b.
mc041-3.jpg
c.
mc041-4.jpg
d.
mc041-5.jpg
e.
mc041-6.jpg
 

 42. 

Find the first and second derivatives of the function.

mc042-1.jpg
a.
mc042-2.jpg
b.
mc042-3.jpg
c.
mc042-4.jpg
d.
mc042-5.jpg
e.
mc042-6.jpg
 

 43. 

During the construction of an office building, a hammer is accidentally dropped from a height of 256 ft. The distance the hammer falls in t sec is mc043-1.jpg. What is the hammer's velocity when it strikes the ground? What is its acceleration?
a.
mc043-2.jpg
b.
mc043-3.jpg
c.
mc043-4.jpg
d.
mc043-5.jpg
e.
mc043-6.jpg
 

Numeric Response
 

 44. 

The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the function  nr044-1.jpg  where t is measured in years, with t = 0 corresponding to the beginning of 1980.

Compute nr044-2.jpg. Round your answer to the nearest thousandth.

nr044-3.jpg__________% per year in the second power

 

Short Answer
 

 45. 

Let sa045-1.jpg

Find the derivative sa045-2.jpg of sa045-3.jpg.

sa045-4.jpg__________

Find the equation of the tangent line to the curve at the point sa045-5.jpg.

__________

Select the correct graph of sa045-6.jpg by answering A, B, or C.

__________

sa045-7.jpg

sa045-8.jpg

sa045-9.jpg
 

 46. 

Let sa046-1.jpg.

Find the derivative sa046-2.jpg of sa046-3.jpg.

sa046-4.jpg__________

Find the point on the graph of f where the tangent line to the curve is horizontal.

__________

Sketch the graph of f and the tangent line to the curve at the point where the tangent line to the curve is horizontal.

Select the correct graph by entering A, B, or C

__________

sa046-5.jpg

sa046-6.jpg

sa046-7.jpg

Let sa046-8.jpg represent the point on the graph of f where the tangent line to the curve is horizontal. What is the rate of change of f at this point?

sa046-9.jpg __________
 

 47. 

Find the derivative of the function.

sa047-1.jpg
 

 48. 

Find the derivative of the function.

sa048-1.jpg
 

 49. 

Find the derivative of the function.

sa049-1.jpg
 

 50. 

Find the derivative of the function.

sa050-1.jpg
 

 51. 

Find the derivative of the function.

sa051-1.jpg
 

 52. 

Find sa052-1.jpg.

sa052-2.jpg
 

 53. 

Find the first and second derivatives of the function.

sa053-1.jpg
 

 54. 

Find the third derivative of the function.

sa054-1.jpg
 



 
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