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.

 a. b. c. d.

2.

Let

Find the equation of the tangent line to the curve at the point .
 a. b. c. d.

3.

Let .

Find the derivative of and the point on the graph of where the tangent line to the curve is horizontal.
 a. b. c. d.

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 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

Find the rate of population growth at 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 and , respectively, where s is measured in feet and t is measured in seconds (see the accompanying figure).

Which car is traveling faster at ?
 a. Car A is traveling faster at , car A is traveling faster at , cars are traveling at the same speed at b. Car B is traveling faster at , car A is traveling faster at , car A is traveling faster at c. Cars are traveling at the same speed at , car A is traveling faster at , car B is traveling faster at d. Car B is traveling faster at , cars are traveling at the same speed at , car A is traveling faster at

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 , where N(t) denotes the population at the end of year t.

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

8.

Let  .

Find the values of x for which .
 a. b. c. d. e.

9.

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

 a. b. c. d. e.

10.

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

 a. b. c. d. e.

11.

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

 a. b. c. d.

12.

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

 a. b. c. d.

13.

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

 a. b. c. d.

14.

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

 a. b. c. d.

15.

Let . Find .
 a. b. c. d.

16.

Let

Find the point(s) on the graph of f where the tangent line is horizontal.
 a. b. c. d.

17.

Retail revenue each year from Internet shopping is approximated by the function
, where is measured in billions of dollars and t is measured in years, with 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. b. c. d.

18.

Find the derivative of the function.

 a. b. c. d. e.

19.

Find the derivative of the function.

 a. b. c. d. e.

20.

Find an equation of the tangent line to the graph of the function at the point .

 a. b. c. d. e.

21.

Evaluate at the value of .

 a. b. c. d. e.

22.

Find an equation of the tangent line to the graph of the function  at the point .
 a. b. c. d.

23.

Find the derivative of the function.

 a. b. c. d.

24.

Find the derivative of the function.

 a. b. c. d.

25.

Find the derivative of the function.

 a. b. c. d.

26.

The number of viewers of a television series introduced several years ago is approximated by the function  , 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 . Find given that ,   , .
 a. b. c. d. e.

28.

Find the derivative of the function.

 a. b. c. d.

29.

Find the derivative of the function.

 a. b. c. d.

30.

Find the derivative of the function.

 a. b. c. d.

31.

Find the derivative of the function.

 a. b. c. d.

32.

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is
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 ?
 a. The actual cost of the 301st oven is \$138.12, the marginal cost when is \$138.00 b. The actual cost of the 301st oven is \$118.12,  the marginal cost when is \$36.00 c. The actual cost of the 301st oven is \$118.12,  the marginal cost when is \$120.00 d. The actual cost of the 301st oven is \$18.12,  the marginal cost when is \$156.00 e. The actual cost of the 301st oven is \$138.12,  the marginal cost when 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 . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , .
 a. , , b. , , c. , , d. , , e. , ,

34.

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

What is the marginal cost when and ?
 a. b. c. d.

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 , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded.

Find the marginal revenue function .
 a. b. c. d.

36.

Find the second derivative of the function.

 a. b. c. d. e.

37.

Find the second derivative of the function.

 a. b. c. d. e.

38.

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

Find a general expression for the car's acceleration at any time t.
 a. b. c. d. e.

39.

Find the first and second derivatives of the function.

 a. b. c. d. e.

40.

Find the first and second derivatives of the function.

 a. b. c. d. e.

41.

Find the first and second derivatives of the function.

 a. b. c. d. e.

42.

Find the first and second derivatives of the function.

 a. b. c. d. e.

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 . What is the hammer's velocity when it strikes the ground? What is its acceleration?
 a. b. c. d. e.

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    where t is measured in years, with t = 0 corresponding to the beginning of 1980.

__________% per year in the second power

45.

Let

Find the derivative of .

__________

Find the equation of the tangent line to the curve at the point .

__________

Select the correct graph of by answering A, B, or C.

__________

46.

Let .

Find the derivative of .

__________

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

__________

Let 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?

__________

47.

Find the derivative of the function.

48.

Find the derivative of the function.

49.

Find the derivative of the function.

50.

Find the derivative of the function.

51.

Find the derivative of the function.

52.

Find .

53.

Find the first and second derivatives of the function.

54.

Find the third derivative of the function.