Test Bank for Applied Calculus Brief 6th Edition by Berresford Chapter Derivatives And Their Uses Complete the table and use it to predict the limit, if it exists 6x7 f ( x) x lim f (x) ? x 0.5 x 0.51 f (x) 0.501 0.5001 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) –121 121 141 –141 does not exist Ans: B Find lim x xx 2x without using a graphing calculator or making tables A) B) –5 C) D) E) Ans: D Berresford/Rockett, Brief Applied Calculus, 6e Use properties of limits and algebraic methods to find the limit, if it exists lim –7 8x x 14 A) 14 B) 14 C) 141 D) 149 E) does not lim x –5 A) x 9x 14 x 2x does exist Ans: B not exist Ans: D Use properties of limits and algebraic methods to find the limit, if it exists E ) B) C) Use properties of find the D) limit, if it exists x 13 x29x8 A) 1712 B) 17 12 C) 12 lim x x 32 limits and algebraic methods to D) 1712 E) does not exist Ans: B ©2013 Cengage Learning All Rights Reserved Page 38 Berresford/Rockett, Brief Applied Calculus, 6e Use properties of limits and algebraic methods to find the limit, if it exists lim h0 xh2 9x2 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 A) B) C) –6 D) 41 41 44 45 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) x2 x 5x A) B) for x C) –6 D) –5 E) does not exist Ans: E 10 Find lim f ( x) for x –6+ A) B) –1 C) D) E) –6 f ( x) x + x+6 Ans: D ©2013 Cengage Learning All Rights Reserved Page 39 Berresford/Rockett, Brief Applied Calculus, 6e 11 Find lim f ( x) for the graph of f ( x) given below x 3+ A) B) C) -3 D) inf E) Ans: A 12 Find lim – x –1 A) B) C) D) –1 x +1 E) Ans: C 13 Find lim x 6+ A) B) C) D) E) Ans: –1 x– 62 –6 E ©2013 Cengage Learning All Rights Reserved Page 40 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 x if x –4 92 x f (x ) if x –4 x –4 123 A) discontinuous B) continuous Ans: B 16 Determine whether the given function is continuous If it is not, identify where it discontinuous is y 3x A) B) C) D) 4x discontinuous at discontinuous at discontinuous at discontinuous at x x x5 x 10 E) continuous everywhere Ans: E 17 Determine whether the function is continuous or discontinuous at the given x-value y x2 ,x –7 x4 A) continuous B) discontinuous Ans: A 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 12 32x x A) discontinuous at x B) discontinuous at x1 C) discontinuous at x D) discontinuous at x1 E) continuous everywhere Ans: D Berresford/Rockett, Brief Applied Calculus, 6e P , P , and P , 19 By imagining tangent lines at points positive, zero, or negative at these points A) At P : positive slope state whether the slopes are At P B) : negative slope At P3 : positive slope At P : zero slope At P C) : negative slope At P3 : positive slope At P : zero slope At P D) : positive slope At P3 : negative slope At P : positive slope At P E) : positive slope At P3 : positive slope At P : positive slope At P : negative slope At P3 : negative slope Ans: C 20 Which graph represents f ( x) if the graph of f ( x) is displayed below? A) B) C) ©2013 Cengage Learning All Rights Reserved Page 44 D) 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) –19 C) 19 D) 13 E) –13 Ans: E 22 Find the average rate of change of f x A) B) C) x between x and x D) 11 E) Ans: A 23 Find the instantaneous rate of change of the function f x A) 6x 5x at x 30 ©2013 Cengage Learning All Rights Reserved Page 45 D) 476 E) 468 Ans: C ©2013 Cengage Learning All Rights Reserved Page 57 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) f ( x ) 15x , f (x ) 30x D) f ( x ) 15x , f (x) 30 E) f ( x ) –10, f (x) Ans: A y 7x 5x 7x 64 Find the third derivative A) B) C) D) E) 42 42x 21 21x Ans: A 65 Find the indicated derivative Find y (4) if y x 8x3 A) 336x5 B) C) 336336xx 48x D) 1680x 48x E) 1680x Ans: E 66 Find f ''(x) for the function x11 A) 994 x 72 B) 99 8x2 x 92 D) 99 16 x2 E) C) 11 11 x Ans: A Berresford/Rockett, Brief Applied Calculus, 6e 67 Find f '''( x) for the function x21 A) 15 399 x2 B) x 15 D) C) 17 x2 E) 17 x2 15 x2 16 Ans: B 68 Find f ( 4) (x) for the function x13 A) 9009 x B) 90094 x 52 C) 1438 x D) 90095 16 x E) 1437 16 x Ans: D 69 Find the second derivative h ( x ) x x 6 A) 42x4 x B) 42x4 42x8 C) 30x4 42x8 D) 42x4 30x4 E) 42 30x x4 Ans: C ©2013 Cengage Learning All Rights Reserved Page 59 Berresford/Rockett, Brief Applied Calculus, 6e 70 Find f ''(5) for the function 4x3 A) B) D) E) 625 500 C) 500 3125 Ans: C 71 Find the third derivative y x23 A) –120 x5 B) 120 x6 C) D) 40 x –120 x6 E) Ans: E 72 2 Find the second derivative of the function (x 3)(x A) x x 21 4x3 8x 12 x 20 12 x x 20 x 21 Ans: D B) C) D) E) 73 d Evaluate the expression A) D) –210 E) 210 Ans: E 3x dx x B) 42 C) –42 7) Berresford/Rockett, Brief Applied Calculus, 6e 74 Find the second derivative of the function A) (2 x 7) B) 112 (2 x 7)3 C) 112 (2 x 7) D) 28 (2 x 7) 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/sec2 C) –80 ft/sec D) 34 ft/sec E) 80 ft/sec Ans: B 76 300 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 77 If f ( g ( x )) x x and f (x) x , find g ( x) Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function A) x B) x C) x x D) x x E) x 3x Ans: D ©2013 Cengage Learning All Rights Reserved Page 61 Berresford/Rockett, Brief Applied Calculus, 6e 78 If f ( g ( x)) x 6x A) and g (x ) 8x 6x , find f ( x) x 8x6 x 6x B) C) D)81x 61x E) x 6x Ans: A 79 If f (g (x)) x f (x ) x and g ( x) A) B) x x C) x x2 D) x 42 E) x x Ans: E x , find Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function 80 Find f (x ) ( x2 1)2 A) x x2 B) x x2 C) x x2 D) x x2 f '( x) for the given function E) x x2 Ans: A 81 y (54x)4 A) 5x B) 4x C) 5x D) 5x E) 20x Ans: C 82 positive Find the derivative of the given function Simplify and express the answer using exponents only 2 (4 x A) 5x C) D) E) y 2) 27(4 x B) 5x 2) 108 x (4 x 5x 108 x (4 x 2) 16 x 5x 2) 5x 8x 2) 16 x 5x 5 27 x (4 x 8x 54 x (4 x 2) 8x Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function Ans: C 83 Differentiate the given function k (x ) 72 (5x x A) 6)14 x 6)13 35x 28(5 x B) 7 13 4(5 x C) x x 6) 35 x D) 4(354(5 x x6 E) 13 2(5 x 13 x 6)151) x6 x 12) 35 x Ans: B ©2013 Cengage Learning All Rights Reserved Berresford/Rockett, Brief Applied Calculus, 6e 84 Differentiate the given function y7x5 3x A) 12 35 x43 1/ B) 12 x 53x 1/ C) 12 D) E) 35 x 7x5 3x 3x 3/ 27x53x 1/ 1/ x5 35 x4 35 x Ans: D 85 Differentiate the given function p q ( q3 7) A) q3 12q2 Page 63 Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function B) 3q2 q7 C) q3 D) 3q2 q37 E) 4q3 q 37 Ans: C 12q2 Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function 86 y (7 x 1) x 17 A) 177 67x 15 B) 171 67x 15 C) 177 7x D) 177 x 15 E) 1 42 x 17 Ans: A Differentiate the given function 87 y A) 6x8 3x B) 52 48 x 73 C) E) 3x 2 x 83 x D) 6x 92 6x8 3x 48 x 6x8 3x x x 48 x7 Page 72 Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function Ans: E 88 Find the derivative of the given function Simplify and express the answer using positive exponents only y x x 7x x 8x 40x A) 21x 128x 56 B) 3 D) C) x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 x 8x 40x 21x 128x 56 E) x 8x 40x 21x 128x 56 Ans: E ©2013 Cengage Learning All Rights Reserved 89 Use the Generalized Power Rule to find the derivative of the function Berresford/Rockett, Brief Applied Calculus, 6e x x4 x 3 x x4 A) B) 2x4 x4 x4 2 x x4 C) x D) x 2x3 E) x 3 x4 1x4 2 Page 73 Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function x Ans: E 90 Differentiate the given function y (6 x) 252 A) (6 x)7 42 B) (6 x)7 252 C) (6 x)7 42 D) (6 x)7 42 E) (6 x)5 Ans: C ©2013 Cengage Learning All Rights Reserved 91 y3 x4 A) 12x5 B) x34 C) 12x4 Page 74 Berresford/Rockett, Brief Applied Calculus, 6e Differentiate the given function D) x35 E) x5 Ans: D 92 A company's cost function is C ( x ) x 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 75 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: 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 –3, 0, –1, none B 0, none –1 –1, E f ( x ) ( x + 2)2 , find the x-value at which the derivative does not For the function exist A B C -2 Page 76 Berresford/Rockett, Brief Applied Calculus, 6e D 79 E none Ans: A ©2013 Cengage Learning All Rights Reserved 97 Use the numerical derivative function on a graphing calculator to calculate the derivative of the function f ( x) at correct? x A 2; No, the calculator is not correct B 0; Yes, the calculator is correct x Is the calculator C 12 ; 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 77