https://getbooksolutions.com Test Bank for Applied Calculus Brief 6th Edition by Berresford Link full download:https://getbooksolutions.com/download/test-bank-forapplied-calculus-brief-6th-edition-by-berresford Chapter Derivatives And Their Uses Complete the table and use it to predict the limit, if it exists 6x f ( x) x lim f (x) x ? 0.5 x 0.51 0.501 0.5001 f (x) 0.5 ? 0.4999 0.499 0.49 A) –160.0 B) 80.0 C) –80.0 D) 0.5 E) does not exist Ans: C Use properties of limits and algebraic methods to find the limit, if it exists lim (8x 13x 3x 13) x A) B) C) D) E) Ans: –121 121 141 –141 does not exist B Find lim x x without using a graphing calculator or making tables x x A) B) –5 C) D) E) Ans: D https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e Use properties of limits and algebraic methods to find the limit, if it exists lim –7 8x x 144x A) 14 B) 14 C) 14 D) 14 E) does not exist Ans: D Use properties of limits and algebraic methods to find the limit, if it exists lim x 9x 14 x 2x x –5 A) B) C) 5 D) E) does not exist Ans: B Use properties of limits and algebraic methods to find the limit, if it exists lim x x 32 x 13 x2 9x A) 17 12 B) C) 17 12 12 17 D) 12 17 E) does not exist Ans: B ©2013 Cengage Learning All Rights Reserved Page 38 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e Use properties of limits and algebraic methods to find the limit, if it exists lim x h h 2 9x h A) B) 2x C) 9x D) 18x E) does not exist Ans: D A graph of y f ( x) is shown and a c-value is given For this problem, use the graph to find lim f ( x) x c c A) B) C) –6 D) –4 E) does not exist Ans: A Use properties of limits and algebraic methods to find the limit, if it exists 16 7x for x lim f (x ), where f (x) x x 5x for x A) B) C) –6 D) –5 E) does not exist Ans: E 10 Find lim f ( x) for x –6 + A) B) C) D) E) Ans: f ( x) x+6 x+6 –1 –6 D ©2013 Cengage Learning All Rights Reserved Page 39 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 11 Find lim f ( x) for the graph of f ( x) given below x A) B) C) D) E) Ans: 12 -3 inf A Find lim x –1 A) B) C) D) E) Ans: 13 + – x +1 –1 C Find lim –1 + x A) B) C) D) E) Ans: x– –6 E ©2013 Cengage Learning All Rights Reserved Page 40 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 14 For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value x A) discontinuous B) continuous Ans: A 15 Determine whether the function is continuous or discontinuous at the given x-value x2 if x –4 f (x ) 9x 123 if x –4 x –4 A) discontinuous B) continuous Ans: B 16 Determine whether the given function is continuous If it is not, identify where it is discontinuous y 3x 4x A) discontinuous at x B) discontinuous at x C) discontinuous at x5 D) discontinuous at x 10 E) continuous everywhere Ans: E 17 Determine whether the function is continuous or discontinuous at the given x-value x2 y ,x –7 x4 A) continuous B) discontinuous Ans: A ©2013 Cengage Learning All Rights Reserved Page 41 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 18 Determine whether the given function is continuous If it is not, identify where it is discontinuous You can verify your conclusions by graphing the function with a graphing utility, if one is available y 8x 3x x 12 A) discontinuous at x B) discontinuous at x1 C) discontinuous at x D) discontinuous at x1 E) continuous everywhere Ans: D ©2013 Cengage Learning All Rights Reserved Page 42 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e P , P , and P , 19 By imagining tangent lines at points state whether the slopes are positive, zero, or negative at these points A) At P : positive slope At P2 : negative slope B) At P3 : positive slope At P : zero slope At P2 : negative slope C) At P3 : positive slope At P : zero slope At P2 : positive slope D) At P3 : negative slope At P : positive slope At P2 : positive slope E) At P3 : positive slope At P : positive slope At P2 : negative slope At P3 : negative slope Ans: C ©2013 Cengage Learning All Rights Reserved Page 43 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 20 Which graph represents f ( x) if the graph of f ( x) is displayed below? A) B) C) D) ©2013 Cengage Learning All Rights Reserved Page 44 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e E) Ans: C 21 For the given function, find the average rate of change over the specified interval f (x ) 5x 4x2 over –2, A) B) C) D) E) Ans: 22 –19 19 13 –13 E Find the average rate of change of f x A) B) C) D) 11 E) Ans: A x between x and x 23 Find the instantaneous rate of change of the function f x 6x A) 30 B) 26 C) 41 D) 42 E) 29 Ans: E ©2013 Cengage Learning All Rights Reserved Page 45 5x at x https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 24 For the function in this problem, find the instantaneous rate of change of the function at the given value f (x ) 9x 5x 5; x A) B) 41 C) 31 D) 67 E) 77 Ans: D 25 For the function in this problem, find the slope of the tangent line at the given value f (x ) 5x 9x 9; x A) B) 14 C) –4 D) E) 19 Ans: A 26 Find the slope of the tangent at x –1 f (x ) 6x 2x A) –14 B) –4 C) –10 D) E) Ans: C 27 For the function in this problem, find the derivative, by using the definition f (x ) 5x 3x A) 5x2 3x B) 5x 3x C) 10x D) 5x E) 10x Ans: E 28 Find the slope of the tangent to the graph of f (x) at any point f (x) 9x2 6x A) 18x B) 18x C) 9x D) x 6x E) 3x Ans: A ©2013 Cengage Learning All Rights Reserved Page 46 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 56 Find the indicated derivative and simplify 6x2 dy for y dx x 4x A) 4 2x 3x x x4 B) 22 x2 4x3x x x4 E) 22 x2 4x 3x x x4 D) 22 x2 2x3x x x4 C) 22 x2 4x 3x x x4 Ans: C 22 x2 57 x Find the derivative of f xx6 A) fx B) 6x5 x 2 x6 x 2x f x 7x6 3 x 3x 4x 2 x2 x6 x2 C) fx D) x 6x5 2 x x6 4x x 2x 2 f x 6x5 x2 x6 x2 E) fx x 7x6 2 x x6 4x x 2x 2 Ans: C ©2013 Cengage Learning All Rights Reserved Page 55 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 58 Find the indicated derivative and simplify f ( x) for f ( x) A) 11x x2 B) C) D) E) 3x x2 x x x2 62 x 18 62 34 x 18 62 3x x2 68 x 18 62 11x x2 34 x 18 68 x 18 62 11x x2 Ans: C 59 Find the derivative of A) B) x–1 1 4x –1 C) D) E) x+1 x – x2 x –1 x x–12 Ans: E ©2013 Cengage Learning All Rights Reserved Page 56 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 60 If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by 2000 p C ( p) , find the rate of change of C with respect to p A) 4000000 130 p B) 260000 130 p C) 16900 130 p D) 2000 130 p E) 130 130 p Ans: B 61 The number of bottles of whiskey that a store will sell in a month at a price of p dollars per bottle is $9 A) B) C) D) E) Ans: 62 N ( p) 2250 Find the rate of change of this quantity when the price is p –18.60 204.55 –18.75 18.50 –9.30 A After x months, monthly sales of a compact disc are predicted to be S(x) x (125 x ) thousand Find the rate of change of the sales after months in thousands per month A) –48 B) 452 C) 420 D) 476 E) 468 Ans: C ©2013 Cengage Learning All Rights Reserved Page 57 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 63 Find f ( x ) and f (x) f (x ) 5x 5x3 A) f ( x ) 15x , f (x )30x B) f ( x ) 30x , f (x) 30 C) D) E) Ans: f ( x ) 15x , f (x ) 30x f ( x ) 15x , f (x) 30 f ( x ) –10, f (x) A 64 Find the third derivative y 7x 5x 7x A) 42 B) 42x C) 21 D) 21x E) Ans: A 65 Find the indicated derivative Find y (4) if y x 8x3 A) 336x B) 336x C) D) 336x 1680x 48x 48x E) 1680x Ans: E 66 Find f ''(x) for the function A) 99 4x B) 99 8x C) 11 2x 99 D) E) 16 x11 2 x 11 x 92 Ans: A ©2013 Cengage Learning All Rights Reserved Page 58 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 67 Find f '''( x) for the function A) x21 15 399 B) x2 15 6783 x C) 17 399 D) x2 15 6783 x 16 E) 17 399 x2 Ans: B 68 Find f ( 4) (x) for the function A) B) C) D) 9009 x 9009 x 13 1438 x 72 9009 16 x E) x 143 16 x Ans: D 69 Find the second derivative h ( x ) x6 x A) B) C) D) E) 42x4 42x4 30x4 42x4 30x4 30 x8 42 x8 42 x8 30 x4 42 x4 Ans: C ©2013 Cengage Learning All Rights Reserved Page 59 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 70 f ''(5) for the function 4x3 A) 625 B) 500 C) 3125 D) 500 E) Ans: C Find 71 Find the third derivative y x2 A) B) C) D) –120 x5 120 x 40 x5 –120 x6 Ans: E E) 72 Find the second derivative of the function (x 3)(x2 A) x x 21 B) 7) 4x 8x C) 12 x 20 D) 12 x2 E) x 20 x 21 Ans: D 73 d x Evaluate the expression dx3 A) B) 42 C) –42 D) –210 E) 210 Ans: E x ©2013 Cengage Learning All Rights Reserved Page 60 https://getbooksolutions.com 74 Berresford/Rockett, Brief Applied Calculus, 6e Find the second derivative of the function x 2x 56 A) (2 x 7)3 112 B) (2 x 7)3 C) 112 (2 x 7)3 D) 28 (2 x 7)2 E) 28 (2 x 7)2 Ans: C 75 If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is s 60 90t 17t What is the acceleration of the object when t 5? A) ft/sec B) –34 ft/sec C) –80 ft/sec D) 34 ft/sec E) 80 ft/sec Ans: B 76 77 300 After t hours, a car is a distance s (t ) 60t t miles from its starting point Find the velocity after hours A) 51 miles/hour B) 66 miles/hour C) 54 miles/hour D) 57 miles/hour E) 63 miles/hour Ans: D x23x If f ( g ( x )) A) x B) x C) D) E) Ans: D x2 x and f (x) x , find g ( x) 3x 3x x 3x ©2013 Cengage Learning All Rights Reserved Page 61 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 78 If f ( g ( x)) A) B) C) x 6x 6x , find f ( x) x 8x x 6x D) x x E) 8x Ans: A 2 6x 79 x If f (g (x)) A) and g (x ) 8x and f (x ) x , find g ( x) x x B) x x C) D) x 2 x E) x x4 Ans: E 80 Find f '( x) for the given function f (x ) ( x2 1)2 A) B) C) D) x x2 x x2 x x2 x x2 E) x x2 Ans: A ©2013 Cengage Learning All Rights Reserved Page 62 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 81 Differentiate the given function y (54x) A) B) C) D) E) 5x 4x 5x 5x 20x Ans: C 82 Find the derivative of the given function Simplify and express the answer using positive exponents only y A) B) C) D) E) (4 x 27(4 x x2 108 x (4 x 2)6 5x 5x 2) 8x 2) 5 16 x 54 x (4 x 5x 2) 8x 27 x (4 x 5x 2) 16 x 108 x (4 x 5x 2) 5 5 8x Ans: C 83 Differentiate the given function k (x ) 72 (5x x 6)14 A) 13 28(5 x B) C) D) E) 4(5 x 4(35x 4(5 x 2(5 x x 6) x 6) 13 35x 35 x x 13 1) x 6)15 x6 x 12) 13 35 x Ans: B ©2013 Cengage Learning All Rights Reserved Page 63 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 84 Differentiate the given function y 7x5 A) B) C) D) 3x 35 x43 1/ 2 x 53x 1/ 1 35 x 7x5 E) 3x 3x 27x53x 1/ 1/ 3/ x5 35 x4 35 x4 Ans: D 85 Differentiate the given function p q ( q 7) A) 12q q3 B) 3q q37 C) 12q q3 D) 3q q37 E) 4q q37 Ans: C ©2013 Cengage Learning All Rights Reserved Page 64 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 86 Differentiate the given function y (7 x 1) 7x 17 A) 17 B) 17 C) 17 D) E) 17 67x 15 67x 15 7x 16 x 15 42 x 1 17 Ans: A 87 Differentiate the given function y (6 x x 1)7 / A) 6x8 3x 2 B) C) 48 x 73 x 83 x D) E) 6x 3x 48 x7 6x8 3x 6x8 x x 48 x7 3x Ans: E 88 Find the derivative of the given function Simplify and express the answer using positive exponents only y x x 7x A) B) C) D) E) x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 Ans: E ©2013 Cengage Learning All Rights Reserved Page 65 https://getbooksolutions.com 89 A) Berresford/Rockett, Brief Applied Calculus, 6e Use the Generalized Power Rule to find the derivative of the function x 2x 3x B) x 2x4 x4 x4 C) x x4 x4 D) 2x3 x4 x E) x 3 x4 x4 Ans: E 90 Differentiate the given function y (6 x)6 A) 252 B) (6 x) 42 7 (6 x) C) 252 (6 x) D) 42 (6 x) E) 42 (6 x)5 Ans: C ©2013 Cengage Learning All Rights Reserved Page 66 x4 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 91 Differentiate the given function y x4 A) 12 x5 B) x C) 12 x4 D) x E) x Ans: D 92 A company's cost function is C ( x ) x2 800 dollars, where x is the number of units Find the marginal cost function and evaluate it for x 30 Round your answer to two decimal places A) 1.18 dollars B) 2.35 dollars C) 50.99 dollars D) 17.65 dollars E) 66.33 dollars Ans: A 93 If $1800 is deposited in a bank paying r% interest compounded annually, years later its value will be V (r ) 1800(1 0.01r)5 dollars Find V '(8) Round your answer to nearest cent A) 122.44 dollars B) 132.24 dollars C) 24.49 dollars D) 26.45 dollars E) 142.82 dollars Ans: A ©2013 Cengage Learning All Rights Reserved Page 67 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 94 For the function displayed in the graph below, find all x-values at which the derivative does not exist A) B) C) D) E) Ans: –3, 0, –1, none B 95 For the function displayed in the graph below, find all x-values at which the derivative does not exist A) B) C) D) E) Ans: 96 0, none –1 –1, E For the function f ( x ) ( x + 2)2 , find the x-value at which the derivative does not exist A) - B) C) D) E) none Ans: A ©2013 Cengage Learning All Rights Reserved Page 68 https://getbooksolutions.com Berresford/Rockett, Brief Applied Calculus, 6e 97 Use the numerical derivative function on a graphing calculator to calculate the at x Is the calculator correct? derivative of the function f ( x) x2 A) 2; No, the calculator is not correct B) 0; Yes, the calculator is correct C) ; No, the calculator is not correct D) 0; No, the calculator is not correct E) 2; Yes, the calculator is correct Ans: D 98 If a function is continuous at a point, then it is also not defined at that same point? A) True B) False Ans: B ©2013 Cengage Learning All Rights Reserved Page 69