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

Chapter is t2 2 B)  C) D) t t t Difficulty: moderate Section: 2.1 The derivative of f (t )  t Ans: B A)  is t8 –8 –8 A) B) C) D) t t t t Ans: A Difficulty: moderate Section: 2.1 The derivative of f (t )  is x 1 A)  B) C)  D)  x x x3 x3 Ans: A Difficulty: moderate Section: 2.1 The derivative of f ( x)  is x –3 –3 A) B) C) D) –3 x 3 x x x Ans: A Difficulty: moderate Section: 2.1 The derivative of f ( x)  True or False: The derivative of f ( x)  x  is 2x + Ans: False Difficulty: easy Section: 2.1 True or False: The derivative of f ( x)  x  is 2x + Ans: False Difficulty: easy Section: 2.1 The equation of the line tangent to the graph of f ( x)  x  3x at x = is A) y = 7x – B) y = 7x – 422 C) y = 7x – D) y = 7x – 144 Ans: A Difficulty: moderate Section: 2.1 The equation of the line tangent to the graph of f ( x)  x  x at x = is A) y = 20x – 36 B) y = 20x – 1728 C) y = 20x – D) y = 20x – 216 Ans: A Difficulty: moderate Section: 2.1 Page 21 Chapter 2  at x = has slope  x 27 Section: 2.1 True or False: The tangent to the graph of f ( x)  Ans: True Difficulty: moderate  at x = has slope of  x 27 Section: 2.1 10 True or False: The tangent to the graph of f ( x)  Ans: True Difficulty: moderate 11 The equation of the line tangent to the graph of f ( x)  x at x = is 1 1 3 A) y  x  B) y  x  C) y  x  D) y  x  2 2 2 Ans: C Difficulty: moderate Section: 2.1 12 True or False: The tangent to the graph of f ( x)  x  at x = has slope Ans: False Difficulty: moderate Section: 2.1 13 True or False: The tangent to the graph of f ( x)  x  at x = has slope of Ans: False Difficulty: moderate Section: 2.1 14 For f(x) = – x2, find the slope of the secant line connecting the points whose xcoordinates 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: Difficulty: moderate Section: 2.1 , find the average rate of change of f(x) with respect to x as x changes x 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 15 For f ( x)   16 If f(x) represents the price per barrel of oil in terms of time, what does f ( x0  h)  f ( x0 ) h f ( x0  h)  f ( x0 ) ? h 0 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 represent? What about lim Page 22 Chapter 17 A spherical balloon is being filled with air in such a way that its radius is increasing at the constant rate of 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 V   r and surface area S  4 r ) Ans: 8 cm /sec Difficulty: hard Section: 2.1 18 True or False: Differentiating f ( x)  x3  3x  gives 3x Ans: False Difficulty: easy Section: 2.2 19 True or False: Differentiating f ( x)  x  x  gives 2x1 Ans: False Difficulty: easy Section: 2.2 20 Differentiate f ( x)  x8  A) x  B) x9  x C) 8x D) 7x Ans: C Difficulty: easy Section: 2.2 21 Differentiate: f ( x)  x8  A) 8x B) x  C) x9  x D) 7x Ans: A Difficulty: easy Section: 2.2 x6  10 x  x  x5  x  gives 3 Section: 2.2 22 True or False: Differentiating f ( x)  Ans: True Difficulty: easy 23 True or False: Differentiating f ( x)  x  x  x  gives x  x3  3 Ans: True Difficulty: easy Section: 2.2 24 True or False: The equation of the line tangent to the graph of f ( x)  x  that passes through (1, 4) is y = 2x + Ans: False Difficulty: moderate Section: 2.2 25 True or False: The equation of the line tangent to the graph of f ( x)  x  that passes through (9, 9) is 2x + Ans: False Difficulty: moderate Section: 2.2 Page 23 Chapter , differentiate f(x) x 1 Ans: f ( x)   3 3x 2x Difficulty: moderate Section: 2.2 26 If f ( x)  x  27 Differentiate f ( x)  x  A) B) x C) Ans: D  D) x x x Difficulty: easy Section: 2.2 28 Differentiate: f ( x)  x  A) x  29 Differentiate: f ( x)  x  –67 23 x  x Difficulty: moderate x3 x B) C) D) x x Ans: A Difficulty: easy  x Section: 2.2  x3 x Ans: Section: 2.2 5x x    x 3x Ans: f ( x)  x5    3x x Difficulty: easy Section: 2.2 30 Differentiate f ( x)  1 x  x  x 2x 1 x– Ans: x    2x Difficulty: easy Section: 2.2 31 Differentiate: f ( x)  32 Find the equation of the tangent line to the curve f ( x)  x3  x  at the point (1, 8) Ans: y = x + Difficulty: moderate Section: 2.2 Page 24 Chapter 33 Find the equation of the tangent line to the curve f ( x)  x3  x  at the point (1, 1) Ans: y = x Difficulty: moderate Section: 2.2 34 Find the equation of the tangent to the graph of f ( x)  x  x  16 at the point (1, 8) Ans: y = –7x + 15 Difficulty: moderate Section: 2.2 35 Find the equation of the tangent to the graph of f ( x)  x  x  at the point (1, 12) Ans: y = 2x + Difficulty: moderate Section: 2.2 36 Find the equation of the tangent line to the graph of f ( x)  x  at (1, 2) A) Not defined B) y = C) x = D) y = 2x Ans: D Difficulty: moderate Section: 2.2 37 Find the equation of the tangent line to the graph of f ( x)  x  at the point (4, 20) A) y = 8x – 12 B) Not defined C) y = 20 D) x = Ans: A Difficulty: moderate Section: 2.2 38 Find the equation of the line that is tangent to the curve f ( x)   3x  x5 at the point (1, 7) Ans: y = x + Difficulty: moderate Section: 2.2 39 Find the equation of the line that is tangent to the curve f ( x)   x  x at the point (1, 17) Ans: y = 16x + Difficulty: moderate Section: 2.2 at x x D) y   40 Find the equation of the tangent line to the graph of f ( x)  x x A) y    B) y    Ans: A Difficulty: moderate C) y = –x +  1  2,   2 Section: 2.2 at the point x D) y  x  7 41 Find the equation of the tangent line to the graph of f ( x)  2 B) y   x  C) y  x x 49 7 49 Ans: A Difficulty: moderate Section: 2.2 A) y   Page 25  1  7,   7 Chapter 42 Find the equation of the tangent line to the curve f ( x)  Ans: y = –5x + Difficulty: moderate Section: 2.2 43 Find the equation of the tangent line to the curve f ( x)  Ans: y = –5x + Difficulty: moderate  x at the point where x = x  x at the point where x = x Section: 2.2 44 The gross national product (GNP) of a certain country is N (t )  t  3t  121 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 Difficulty: hard Section: 2.2 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 Q(t )  0.07t  0.2t  2.8 ppm The rate that the carbon monoxide level will change with respect to time 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 E (t )  0.2t  9t  30 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 Q(t )  0.05t  0.3t  3.2 parts per million (ppm) The rate that the carbon monoxide level will change with respect to time 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)  0.01x3  x  3x  200 refrigerators will be sold per month Find R(4) and interpret what it tells us about sales R(4)  203.36; they'll sell about 203 refrigerators if they run ads per day A) R(4)  4.52; they'll sell about refrigerators if they run ads per day B) R(4)  4.52; sales will be increasing at about refrigerators per month per ad C) when they're running ads R(4)  203.36; the cost of refrigerators will be rising by $203.36 if they're selling D) per day Ans: C Difficulty: easy Section: 2.2 Page 26 Chapter 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 )  t  6t  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 Difficulty: hard Section: 2.2 50 Find all points (x, y) on the graph of the function y  5x 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) Ans: C Difficulty: moderate Section: 2.2 51 If the position of an object moving along a straight line is given by s(t )  t  7t  6t at time t, find the object's velocity as a function of time A) C) v(t )  3t  7t  v(t )  t  7t  B) D) v(t )  t  14t v(t )  3t  14t  Ans: D Difficulty: moderate Section: 2.2 52 The displacement function of a moving object is described by s(t )  t  5t  What is the object's acceleration? A) 2t + B) 2t C) t D) Ans: D Difficulty: hard Section: 2.2 53 The displacement function of a moving object is described by s(t )  t  2t  What is the acceleration of the object as a function of time? A) B) 2t + C) 2t D) t Ans: A Difficulty: moderate Section: 2.2 54 The displacement function of a moving object is described by s(t )  t  2t  What is the velocity of the object as a function of t? A) 3t B) 3t  C) D) 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  27t  195t  Find the velocity and acceleration of the object at time t When is the object stationary? A) v(t )  3t  54t  195 ; a(t) = 6t – 54; t = and 13 B) v(t )  3t  54t  195 ; a(t) = 6t – 54; t = C) v(t )  3t  18t  195 ; a(t) = 6t – 18; t = D) v(t )  3t  54t  195 ; a(t) = 6t – 54; t = Ans: A Difficulty: moderate Section: 2.2 Page 27 Chapter 56 The displacement function of a moving object is described by s(t )  t  2t  What is the velocity of the object as a function of time? A) 3t  B) 3t C) D) Ans: A Difficulty: easy Section: 2.2 57 True or False: If the displacement of a moving object is s(t )  t , the acceleration is 6t Ans: True Difficulty: easy Section: 2.2 58 True or False: If the displacement of a moving object is s(t )  6t , the acceleration is 36t Ans: True Difficulty: easy Section: 2.2 59 If an object moves in such a way that after t seconds, the distance from its starting point is D(t )  t  15t  80t meters, find the acceleration after seconds in meters/s Ans: –18 meters/s2 Difficulty: hard Section: 2.2 60 Differentiate f ( x)  ( x  1)( x  3) A) 2x + B) 6x + C) x  x  D) x  Ans: C Difficulty: moderate Section: 2.3 61 Differentiate: f ( x)  ( x  4)( x  2) A) 3x  x  B) 2x + C) 16x + D) x  Ans: A Difficulty: moderate Section: 2.3 62 What is the rate of change of f (t )  3t  with respect to t when t = 4? t4 15 15 B) C) D) 64 8 Ans: A Difficulty: hard Section: 2.3 A) 2x 1 , what is f ( x) ? 7x  19 Ans: f ( x )  (7 x  6) Difficulty: moderate Section: 2.3 63 If f ( x)  Page 28 Chapter x2 x2 2 x  4x x  4x A) B) C) 2x D) –x ( x  2) ( x  2) Ans: A Difficulty: moderate Section: 2.3 64 Differentiate f ( x)  x2 65 Differentiate: f ( x)  x 1 x2  2x 3x  x A) B) C) 2x D) –x 2  x  1  x  1 Ans: A Difficulty: moderate Section: 2.3  3x 66 If f ( x)  , what is f ( x) ? x  2x  3x  12 x  24 x  Ans: f ( x)  ( x3  x  4) Difficulty: hard Section: 2.3 67 True or False: The equation of the line that is tangent to the curve f ( x)  (3x5  x  5)( x3  x  1) at the point (0, –5) is y = 5x – Ans: True Difficulty: hard Section: 2.3 68 True or False: The equation of the tangent line to the curve f ( x)  (6 x5  x  4)( x3  x  1) at the point (0, –4) is y = 4x – Ans: True Difficulty: hard Section: 2.3 69 If f ( x)  Ans: 3x  , what is f ( x) ? x 1  x  1 Difficulty: moderate Section: 2.3 70 Find the equation of the line that is tangent to the curve f ( x)  (1, –1) Ans: y = –9x + Difficulty: hard Section: 2.3 Page 29 5x2  x  at the point  x3 Chapter 2  3x , what is f ( x) ? x3  x  3x  x  x  71 If f ( x)  Ans: x  x  1 Difficulty: hard Section: 2.3 72 Find the equation of the tangent line to the curve f ( x )  4x2  6x  at the point (1, 2)  x3 Ans: y = 14x – 12 Difficulty: hard Section: 2.3 73 What is the rate of change of f (t )  2t  with respect to t when t = 5? t 5 17 C) 10 D) 10 10 Difficulty: hard Section: 2.3 13 100 Ans: A A) B) 74 What is the rate of change of f (t )  6t  with respect to t when t = 18? t 3 1 B)  C) 21 D) –21 21 21 Ans: A Difficulty: hard Section: 2.3 A) 75 Find the equation of the normal line to f ( x)  x3  x  51 at the point with x-coordinate –2 701 Ans: y   x  52 26 Difficulty: moderate Section: 2.3 76 Find an equation for the tangent line to the curve y   x at the point where x = –1 5 19 x 30 30 Difficulty: hard Section: 2.3 Ans: y  77 Find f ( x) , where f ( x)  Ans: 18 x 1  x3   x3 1  x  3 Difficulty: hard Section: 2.3 Page 30 Chapter 78 Find f ( x) , where f ( x)  x3  Ans: 6x Difficulty: easy Section: 2.3 79 The temperature in degrees Fahrenheit inside an oven t minutes after turning it on can be modeled with the function 400t  70 Find F (5) and interpret what it tells us about the temperature F (t )  t 1 Round your answer to decimal places Ans: F (5)  9.17 ; After minutes, the temperature is increasing at the rate of 9.17 degrees per minute Difficulty: easy Section: 2.3 80 It is estimated that t years from now, the population of a certain suburban community will be p(t )  30  thousand people At what rate will the population be growing 7t  years from now? Ans: 29 people/year Difficulty: hard Section: 2.3 81 Find A) B) Ans: f (4) ( x) if f ( x)  x5  x  x3  5x  10 x  20 C) f (4) ( x)  60 x  144 x  12 f (4) ( x)  x  x D) f (4) ( x)  120 x  144 f (4) ( x)  x  x  B Difficulty: moderate Section: 2.3 82 True or False: If f ( x)  3x5  x3  x  , then f ( x)  180 x  42 Ans: True Difficulty: moderate Section: 2.3  3 6x x f ( x )    A) C) 8x 6x x 15 120 f ( x)    B) D) 16 x x x Ans: C Difficulty: moderate Section: 2.3 83 Find f ( x ) if f ( x)  84 Find Ans: dy if y  u and u  x  3x3  dx x3  x 3  x  3x3   Difficulty: hard Section: 2.4 Page 31 120 8x x x 15 120 f ( x)    1728 x x x f ( x)   15  Chapter dy if y  u  2u  and u  x  x  dx Ans: x5  15 x  x3  x  x  Difficulty: hard Section: 2.4 85 Find 86 Find dy if y  u  4u  and u  x  x  dx Ans:  x  1  x  x    16 x  24 x  104 x  56 Difficulty: hard Section: 2.4 dy if y  u and u  x  3x3  dx x3  x Ans: 3( x  3x3  2)2 / Difficulty: hard Section: 2.4 87 Find 88 Find Ans: dy 1 if y  and u  dx 3u  x2 1  x  Difficulty: hard 89 Find Ans: Section: 2.4 dy 1 if y  and u  dx 8u  x6  x  2 Difficulty: hard Section: 2.4 (3  x)3 , then f ( x)  5(2 x  1) ( x  x  1)2 Difficulty: moderate Section: 2.4 90 True or False: If f ( x)  Ans: False 2x  x  3x  , then f ( x)   3x  3x Difficulty: moderate Section: 2.4 91 True or False: If f ( x)  Ans: False 92 True or False: An equation for the tangent line to the curve f ( x)  3x  x at the point where x = is y  x  Ans: False Difficulty: moderate Section: 2.4 Page 32 Chapter 93 An equation for the tangent line to the curve y  ( x  x  1)3 at the point where x = is: A) y = 9x – B) y = 9x C) y = 2x + D) y = 9x – Ans: A Difficulty: moderate Section: 2.4 94 Find an equation for the tangent line to the curve y  (7 x  x  1)3 at the point where x = A) y = 14x + B) y = 24x + C) y = 3x + D) y = 3x – Ans: D Difficulty: moderate Section: 2.4 95 An equation for the tangent line to the curve y  ( x5  x  1)4 at the point where x = is A) y = 24x – 23 B) y = 24x C) y = 5x + D) y = 24x – Ans: A Difficulty: moderate Section: 2.4 96 An equation for the tangent line to the curve y  (8x  x  1)5 at the point where x = is A) y = 5x – B) y = 10x + C) y = 5x + D) y = 10x – Ans: A Difficulty: moderate Section: 2.4 97 True or False: An equation for the tangent line to the curve f ( x)  x3 (1  3x)2 at the point where x = –1 is y = 72x + 56 Ans: True Difficulty: moderate Section: 2.4 98 Find an equation for the tangent line to the curve y   x at the point where x = –1 Ans: y = 0.11x + 1.42 Difficulty: hard Section: 2.4 99 Find all points on the graph of the function f ( x)  x  x  16  where the tangent line is horizontal Ans: (0, 0) and (–3, –108) Difficulty: moderate Section: 2.4 100 Find all points on the graph of the function f ( x)  x2 where the tangent line is x2 horizontal A) There are none B) (2, 1) C) (0, 0) and (–4, –8) Ans: C Difficulty: moderate Section: 2.4 D) (0, 0) 101 True or False: If f ( x)  x  x , then f ( x)  at x = and x = Ans: False Difficulty: hard Section: 2.4 Page 33 Chapter 3 (1  x )3/ Section: 2.4 102 True or False: If f ( x)   3x , then f "( x)  Ans: False Difficulty: moderate 103 If g ( y )  y  y represents the height in inches of a sapling y weeks after germination, find g (5) and interpret what it tells us about the height of the tree Round your answer to decimal place Ans: after weeks, the tree is growing at 1.1 inches per week Difficulty: easy Section: 2.4 104 At a certain factory, the total cost of manufacturing q units during the daily production run is C (q)  0.3q  0.8q  800 dollars It has been determined that approximately q(t )  t  80t units are manufactured during the first t hours of a production run Compute the rate at which the total manufacturing cost is changing with respect to time hours after production begins Ans: It is increasing at $8,332.80/hour Difficulty: hard Section: 2.4 57, 600 p toasters a month It is estimated that t months from now, the price of the toasters will be p(t )  0.03t 3/  22.08 dollars Compute the rate at which the monthly demand for the toasters will be changing with respect to time 16 months from now Ans: Decreasing by 18 toasters/month Difficulty: hard Section: 2.4 105 When toasters are sold for p dollars apiece, local consumers will buy D ( p )  106 True or False: When a certain commodity is sold for p dollars per unit, consumers will 30, 000 buy D ( p )  units per month It is estimated that t months from now, the price of p the commodity will be p(t )  0.3t 5/  5.4 dollars per unit The monthly demand will be decreasing 40 months from now Ans: True Difficulty: hard Section: 2.4 107 When a certain commodity is sold for p dollars per unit, consumers will buy 31,500 D( p)  units per month It is estimated that t months from now, the price of the p commodity will be p(t )  t 2/  5.15 dollars per unit The approximate rate at which the monthly demand will be changing with respect to time in 27 months is A) –35 units per month C) –31.5 units per month B) 35 units per month D) –131.5 units per month Ans: A Difficulty: hard Section: 2.4 Page 34 Chapter 108 It is estimated that t years from now, the population of a certain suburban community will be p(t )  50  thousand people At what rate, in people/year will the population be 2t  growing years from now? Ans: 285.7 people/year Difficulty: hard Section: 2.4 109 True or False: It is estimated that t years from now, the population of a certain suburban community will be p(t )  30  thousand An environmental study indicates that 2t  the average daily level of carbon monoxide in the air will be C ( p)  0.3 p  p  30 parts per million (ppm) when the population is p thousand The rate at which the level of pollution is changing with respect to time years from now is about 0.084 ppm per year Ans: True Difficulty: hard Section: 2.4 110 It is estimated that t years from now, the population of a certain community will be thousand An environmental study indicates that the average daily level p(t )  14  3t of carbon monoxide in the air will be C ( p)  0.5 p  p  30 units when the population is p thousand The rate at which the level of carbon monoxide will be changing years from now is A) –0.078 ppm per thousand people C) 1.000 ppm per thousand people B) 0.078 ppm per thousand people D) –1.000 ppm per thousand people Ans: B Difficulty: hard Section: 2.4 111 True or False: The function f ( x)  decreases from to 2.7 Ans: False Difficulty: hard x  will decrease by approximately 0.6 as x 2x 1 Section: 2.5 112 The largest percentage error you can allow in the measurement of the radius of a sphere if you want the error in the calculation of its surface area using the formula S  4 r to be no greater than percent is about: A) 6% B) 3% C) 1% D) 2% Ans: B Difficulty: hard Section: 2.5 Page 35 Chapter 113 You measure the side of a cube to be 11 centimeters long and conclude that the volume of the cube is 113  1,331 cubic centimeters If your measurement of the side is accurate to within 2% , approximately how accurate is your calculation of this volume? A) Maximum error in volume is about ± 7.26 cm B) Maximum error in volume is about ± 79.86 cm C) Maximum error in volume is about ± 0.66 cm D) Maximum error in volume is about ± 878.46 cm Ans: B Difficulty: moderate Section: 2.5 114 If the total cost of manufacturing q units of a certain commodity is C(q) = (3q + 1)(5q + 7), use marginal analysis to estimate the cost of producing the 19th unit, in dollars Ans: 596 dollars Difficulty: hard Section: 2.5 115 An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 8:00 A.M will have assembled f ( x)   x3  8x  x transistor radios x hours later Approximately how many radios will the worker assemble between 11:00 and 11:45 A.M.? A) Approximately 19 radios C) Approximately 14 radios B) Approximately 855 radios D) Approximately 39 radios Ans: C Difficulty: moderate Section: 2.5 116 True or False: If x3  y3  x  y , then Ans: False Difficulty: moderate dy 3x   dx y  Section: 2.6 dy , where xy  3x  y dx x  y3 6x A) y  x  B) C) D) y  x 3xy  y3 Ans: B Difficulty: moderate Section: 2.6 117 Find 118 Find dy , where dx x  y  xy   x 1  x y  y x y 1 Ans: Difficulty: moderate Section: 2.6 Page 36 Chapter dy 5 , where  x 2y dx y2 Ans:  x Difficulty: moderate Section: 2.6 119 Find dy  2x  3y dx Section: 2.6 120 True or False: If x  3xy  y  15 , then Ans: False Difficulty: moderate 121 True or False: If x y  xy  , then Ans: False Difficulty: moderate dy  xy  y dx Section: 2.6 dy  2x dx Difficulty: moderate Section: 2.6 122 True or False: If x  y  , then Ans: False 123 Find an equation for the tangent line to the curve x3  xy  y  x at the point (1, 0) Ans: y = –2x + Difficulty: hard Section: 2.6 124 Find the slope of the tangent line to the curve x  3xy  y  at the point (1, 1) A) B) C) –5 D) Ans: C Difficulty: hard Section: 2.6 125 Find an equation for the tangent line to the curve x  y  xy  at the point (1, –1) Ans: y   x  2 Difficulty: hard Section: 2.6 126 Find the equation of the tangent line to the given curve at the specified point: x3 y  xy  3x  y  11 ; (0, 11) 1 x  11 B) y   x  11 C) y = –47x + 11 D) y = 47x + 11 A) y  47 47 Ans: C Difficulty: moderate Section: 2.6 127 True or False: The equation for the tangent line to the curve x  xy  y at the point (1, –1) is y = –1 Ans: True Difficulty: hard Section: 2.6 Page 37 Chapter 128 Use implicit differentiation to find A) 80x3 Ans: B 129 Find Ans: d2y for x5  11y  100 dx 80 C) 60 x  11 D) 60 x  100 x 11 Difficulty: easy Section: 2.6 B)  dy , where ( x  y)3  y  dx 3 x  3y  9 x  3y 1 Difficulty: moderate Section: 2.6 130 In a certain factory, output Q is related to inputs x and y by the equation Q  3x3  x y  y If the current levels of input are x = 255 and y = 155, use calculus to estimate the change in input y that should be made to offset a decrease of 0.6 unit in input x so that output will be maintained at its current level A) An increase of 0.37 C) It cannot be determined B) A decrease of 0.37 D) No change Ans: A Difficulty: moderate Section: 2.6 131 The output at a certain plant is Q  0.06 x  0.15 xy  0.05 y units per day, where x is the number of hours of skilled labor used and y is the number of hours of unskilled labor used Currently 60 hours of skilled labor and 150 hours of unskilled labor are used each day Use calculus to estimate the change in unskilled labor that should be made to offset a hour increase in skilled labor so that output will remain the same A) An increase of 1.24 hours C) It cannot be determined B) A decrease of 1.24 hours D) No change Ans: B Difficulty: hard Section: 2.6 132 Suppose the output at a certain factory is Q  x  5x1 y1  y1 units, where x is the number of hours of skilled labor used and y is the number of hours of unskilled labor The current labor force consists of 30 hours of skilled labor and 30 hours of unskilled labor Use calculus to estimate the change in unskilled labor y that should be made to offset a 1hour increase in skilled labor x so that output will be maintained at its current level A) –2.55 hours B) –1.76 hours C) –0.39 hours D) 0.39 hours Ans: A Difficulty: moderate Section: 2.6 Page 38 ... 2.1 14 For f(x) = – x2, find the slope of the secant line connecting the points whose xcoordinates are x = –4 and x = –3.9 Then use calculus to find the slope of the line that is tangent to the. .. points (x, y) on the graph of the function y  5x 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)... 35 Find the equation of the tangent to the graph of f ( x)  x  x  at the point (1, 12) Ans: y = 2x + Difficulty: moderate Section: 2.2 36 Find the equation of the tangent line to the graph