Applied calculus for business economics and the social and life sciences expanded 10th edition hoffmann test bank

Ans: False Difficulty: moderate Section: 2.1 13.. Ans: False Difficulty: moderate Section: 2.1 14.. Difficulty: easy Section: 2.1... Ans: False Difficulty: moderate Section: 2.2 25.. Ans

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Chapter 2

1 The derivative of f t( ) 12

t

 is

A) 2

t

 B) 23

t

 C) 2

t D) 3

1

t

Ans: B Difficulty: moderate Section: 2.1

2 The derivative of f t( ) 18

t

 is

A) –89

t B) 7

–8

t C) 7

8

t D) 9

1

t

Ans: A Difficulty: moderate Section: 2.1

3 The derivative of f x( ) 2

x

 is

A)

3

1

x

 B)

3

1

x

C) 1

x

 D)  x

4 The derivative of f x( ) 3

x

 is

A)

3

–3

2 x

B)

3

2 x

C) –3

2 x D) –3 x

5 True or False: The derivative of f x( )x2 is 2x + 5 5

Ans: False Difficulty: easy Section: 2.1

6 True or False: The derivative of f x( )x2 is 2x + 5 5

Ans: False Difficulty: easy Section: 2.1

7 The equation of the line tangent to the graph of 2

f x x  x at x = 2 is A) y = 7x – 4 B) y = 7x – 422 C) y = 7x – 2 D) y = 7x – 144

8 The equation of the line tangent to the graph of f x( )x28x at x = 6 is A) y = 20x – 36 B) y = 20x – 1728 C) y = 20x – 6 D) y = 20x – 216

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9 True or False: The tangent to the graph of f x( ) 12 2

x

  at x = 3 has slope 2

27

Ans: True Difficulty: moderate Section: 2.1

10 True or False: The tangent to the graph of f x( ) 12 8

x

  at x = 3 has slope of 2

27

Ans: True Difficulty: moderate Section: 2.1

11 The equation of the line tangent to the graph of ( )f x 3 x at x = 1 is

A) 1 1

y x B) 1 1

y x C) 3 3

y x D) 3 1

2

y x

Ans: C Difficulty: moderate Section: 2.1

12 True or False: The tangent to the graph of ( )f x  x  at x = 2 has slope 3 1

2

Ans: False Difficulty: moderate Section: 2.1

13 True or False: The tangent to the graph of ( )f x  x  at x = 2 has slope of 5 1

2

14 For f(x) = 5 – x2, find the slope of the secant line connecting the points whose

x-coordinates are x = –4 and x = –3.9 Then use calculus to find the slope of the line that is tangent to the graph of f at x = –4

Ans: Slope of secant line: 7.9; Slope of tangent line: 8

Difficulty: moderate Section: 2.1

15 For f x( ) 3

x

  , find the average rate of change of f(x) with respect to x as x changes from 144 to 145 Then use calculus to find the instantaneous rate of change at x = 144

A) Average rate of change: 0.000864; Instantaneous rate of change: –0.125

B) Average rate of change: –0.000864; Instantaneous rate of change: 0.000868 C) Average rate of change: –0.000864; Instantaneous rate of change: 0.125

D) Average rate of change: 0.000864; Instantaneous rate of change: 0.000868 Ans: D Difficulty: hard Section: 2.1

16 If f(x) represents the price per barrel of oil in terms of time, what does f x( 0 h) f x( )0

h

 

represent? What about 0 0

0

lim

h



 

?

Ans: The average rate of change of oil price with respect to time on the time interval [x0,

x0 + h]; the instantaneous rate of change of oil price with respect to time at time x0 Difficulty: easy Section: 2.1

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17 A spherical balloon is being filled with air in such a way that its radius is increasing at the constant rate of 2 cm/sec At what rate is the volume of the balloon increasing at the instant when its surface has area 4 cm2 ? (Note: A sphere of radius r has volume

3

4

3

V  r and surface area S 4r2 )

Ans: 8 cm 3 /sec

Difficulty: hard Section: 2.1

18 True or False: Differentiating 3

f x x  x gives 2

3x Ans: False Difficulty: easy Section: 2.2

19 True or False: Differentiating f x( )x26x gives 5 1

2x Ans: False Difficulty: easy Section: 2.2

20 Differentiate f x( )x8 2

A) 8x 7 2 B) 8x92x C) 8x7 D) 7x7

Ans: C Difficulty: easy Section: 2.2

21 Differentiate: f x( )x8 4

A) 8x7 B) 8x 7 4 C) 8x94x D) 7x7

Ans: A Difficulty: easy Section: 2.2

22 True or False: Differentiating ( ) 1 7 2 5 9 8

3

f x  x  x  x gives

6

4

7

3

x

Ans: True Difficulty: easy Section: 2.2

23 True or False: Differentiating ( ) 1 7 2 4 8 4

3

f x  x  x  x gives 7 6 8 3 8

24 True or False: The equation of the line tangent to the graph of ( )f x  x that passes 3

through (1, 4) is y = 2x + 3

25 True or False: The equation of the line tangent to the graph of ( )f x  x that passes 6

through (9, 9) is 2x + 6

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26 If 3 1

( )

x

  , differentiate f(x)

( )

f x

27 Differentiate f x( ) x 1

x

A) 0 B) x C)

3

2 x 2 x D)

3

2 x 2 x Ans: D Difficulty: easy Section: 2.2

28 Differentiate: f x( ) x 1

x

A)

3

2 x 2 x B) 0 C) 1 D)

3

2 x 2 x Ans: A Difficulty: easy Section: 2.2

29 Differentiate: 7 3

( )

x

Ans: 1 –67 3 23





30 Differentiate 2 6 5 2 5

( )

x

Ans: ( ) 4 5 5 22 14

Difficulty: easy Section: 2.2

31 Differentiate: 2 6 1 1 8

( )

x

Ans:

7

– 5

2

6

x x

x

Difficulty: easy Section: 2.2

32 Find the equation of the tangent line to the curve f x( )x3x2 at the point (1, 8) 8

Ans: y = x + 7

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33 Find the equation of the tangent line to the curve f x( )x3x2 at the point (1, 1) 1

Ans: y = x

34 Find the equation of the tangent to the graph of f x( )x29x at the point (1, 8) 16

Ans: y = –7x + 15

35 Find the equation of the tangent to the graph of 2

f x x  x at the point (1, 12)

Ans: y = 2x + 9

36 Find the equation of the tangent line to the graph of f x( )x2 at (1, 2) 1

A) Not defined B) y = 2 C) x = 1 D) y = 2x

Ans: D Difficulty: moderate Section: 2.2

37 Find the equation of the tangent line to the graph of f x( )x2  at the point (4, 20) 4

A) y = 8x – 12 B) Not defined C) y = 20 D) x = 4

38 Find the equation of the line that is tangent to the curve f x( ) 5 3x2 at the point x5

(1, 7)

Ans: y = x + 6

39 Find the equation of the line that is tangent to the curve f x( ) 9 9x2 at the point x2

(1, 17)

Ans: y = 16x + 1

40 Find the equation of the tangent line to the graph of f x( ) 1

x

 at 2,1

2

4

x

2

x

y    C) y = –x + 1 D) 1

2

x

41 Find the equation of the tangent line to the graph of f x( ) 1

x

 at the point 7,1

7

y  x B) 1 2

y  x C) 1

49

y x D) 1 2

y x

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42 Find the equation of the tangent line to the curve f x( ) 4 x

x

  at the point where x = 1 Ans: y = –5x + 8

43 Find the equation of the tangent line to the curve f x( ) 4 x

x

  at the point where x = 1 Ans: y = –5x + 8

44 The gross national product (GNP) of a certain country is 2

N t   t t billion

dollars where t is the number of years after 1990 At what percentage rate will the GNP

be changing with respect to time in 1995?

Ans: 8.07

45 True or False: An environmental study of a certain suburban community suggests that t

years from now the average level of carbon monoxide in the air will be

2 ( ) 0.07 0.2 2.8

Q t  t  t ppm The rate that the carbon monoxide level will change with respect to time 2 years from now will be 0.048 ppm/yr

Ans: False Difficulty: hard Section: 2.2

46 True or False: The gross annual earnings of a certain company were

2 ( ) 0.2 9 30

E t  t  t thousand dollars where t is the number of years since its formation

in 1990 The gross annual earnings with respect to t in 1995 are growing at 13.75%

Ans: True Difficulty: hard Section: 2.2

47 True or False: An environmental study of a certain suburban community suggests that t

years from now the average level of carbon monoxide in the air will be

2 ( ) 0.05 0.3 3.2

Q t  t  t parts per million (ppm) The rate that the carbon monoxide level will change with respect to time 4 years from now will be 0.4 ppm/yr

Ans: False Difficulty: hard Section: 2.2

48 An appliance store manager estimates that for x television ads run per day,

R x   x x  x refrigerators will be sold per month Find R(4) and interpret what it tells us about sales

A) R(4)203.36; they'll sell about 203 refrigerators if they run 4 ads per day

B) R(4)4.52; they'll sell about 5 refrigerators if they run 4 ads per day

C) R(4)4.52; sales will be increasing at about 5 refrigerators per month per ad when they're running 4 ads

D) R(4)203.36; the cost of refrigerators will be rising by $203.36 if they're selling

4 per day

Ans: C Difficulty: easy Section: 2.2

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49 An efficiency study at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M will have produced Q t( )  t3 6t218t units t hours later At

what rate, in units/hour, is the worker's rate of production changing with respect to time

at 9:00 A.M.?

Ans: 27 units/hour

50 Find all points (x, y) on the graph of the function 2

5

y x with the property that the

tangent to the graph at (x, y) passes through the point (4, 0)

A) (0, 0) and (4, 80) B) (4, 80) C) (0, 0) and (8, 320) D) (8, 320)

51 If the position of an object moving along a straight line is given by s t( ) t3 7t2 at 6t

time t, find the object's velocity as a function of time

A) v t( )3t2   7t 6 C) v t( )   t2 7t 6

B) v t( ) t2 14t D) v t( )3t2 14t 6

Ans: D Difficulty: moderate Section: 2.2

52 The displacement function of a moving object is described by s t( )   What is t2 5t 2 the object's acceleration?

A) 2t + 5 B) 2t C) t D) 2

Ans: D Difficulty: hard Section: 2.2

53 The displacement function of a moving object is described by s t( )   What is t2 2t 6 the acceleration of the object as a function of time?

A) 2 B) 2t + 2 C) 2t D) t

54 The displacement function of a moving object is described by s t( )   What is t3 2t 1

the velocity of the object as a function of t?

A) 3t2 B) 3t 2 2 C) 3 D) 2

Ans: B Difficulty: easy Section: 2.2

55 An object moves along a line in such a way that its position at time t is

s t  t t  t  Find the velocity and acceleration of the object at time t

When is the object stationary?

( ) 3 54 195

v t  t  t ; a(t) = 6t – 54; t = 5 and 13

( ) 3 54 195

v t  t  t ; a(t) = 6t – 54; t = 9

( ) 3 18 195

v t  t  t ; a(t) = 6t – 18; t = 5

( ) 3 54 195

v t  t  t ; a(t) = 6t – 54; t = 5

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56 The displacement function of a moving object is described by s t( )   What is t3 2t 3 the velocity of the object as a function of time?

A) 3t 2 2 B) 3t2 C) 3 D) 2

Ans: A Difficulty: easy Section: 2.2

57 True or False: If the displacement of a moving object is s t( ) , the acceleration is 6t t3

58 True or False: If the displacement of a moving object is s t( )6t3 , the acceleration is

36t

59 If an object moves in such a way that after t seconds, the distance from its starting point

D t  t t  t meters, find the acceleration after 2 seconds in meters/s 2 Ans: –18 meters/s2

60 Differentiate f x( )(x21)(x 3)

A) 2x + 1 B) 6x + 1 C) 3x26x1 D) x 2 1

61 Differentiate: f x( )(x24)(x 2)

A) 3x24x4 B) 2x + 1 C) 16x + 1 D) x 2 1

62 What is the rate of change of ( ) 3 3

4

t

f t t





 with respect to t when t = 4?

A) 15

64 B)

15

8 C) 8 D)

7 8

Ans: A Difficulty: hard Section: 2.3

63 If ( ) 2 1

x

f x

x





 , what is f x( ) ? Ans: ( ) 19 2

f x

x



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64 Differentiate

2

( )

2

x

f x

x





A)

2

4

x



 B)

2 2

4

x



 C) 2x D) –x

65 Differentiate:

2

( )

1

x

f x

x





A)

2

2 1

x



 B)  

2 2

1

x



 C) 2x D) –x

66 If

2 3

2 3 ( )

x

f x





  , what is f x( ) ?

Ans:

( )

f x

 

67 True or False: The equation of the line that is tangent to the curve

f x  x  x  x   at the point (0, –5) is y = 5x – 5 x

68 True or False: The equation of the tangent line to the curve

f x  x  x  x   at the point (0, –4) is y = 4x – 4 x

69 If ( ) 3 1

1

x

f x

x





 , what is f x( ) ?

Ans:

4 1

x 

70 Find the equation of the line that is tangent to the curve

2 3

( )

5 4

f x

x



 at the point

(1, –1)

Ans: y = –9x + 8

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71 If

2 3

2 3 ( )

1

x

f x





  , what is f x( ) ?

Ans:

2 3

1

 

72 Find the equation of the tangent line to the curve

2 3

( )

3 2

f x

x



 at the point (1, 2)

Ans: y = 14x – 12

5

t

f t t





A) 13

100 B)

17

10 C) 10 D)

7 10

Ans: A Difficulty: hard Section: 2.3

3

t

f t t





A) 1

21 B)

1 21

 C) 21 D) –21 Ans: A Difficulty: hard Section: 2.3

75 Find the equation of the normal line to 3

f x  x  x at the point with x-coordinate

–2

y  x

76 Find an equation for the tangent line to the curve 2 1

5

y  x at the point where x = –1

77 Find f( )x , where ( ) 3 3

1

f x

x



3 3 3

18 1 2 1

x

 Difficulty: hard Section: 2.3

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