Exam on Hawkes

FALL 2020 - Calculus Remaining Examination Evaluation (Reply Key) 1. Take into account the next one-sided restrict. π’π’Šπ’Ž π‘₯ β†’ 18βˆ’ ( π‘₯ 2 βˆ’ 324 π‘₯ βˆ’ 18 ) Step 1. Approximate the restrict by filling within the desk. Spherical to the closest thousandth. Step 2. Decide the worth of the one-sided restrict. Reply: ____________________ 2. Use the graph of 𝑦 = 𝑓 (π‘₯) to seek out the bounds: Step 1. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’three βˆ’ 𝑓 (π‘₯). Reply: _______________ Step 2. Discover π’π’Šπ’Ž π‘₯ β†’ 1 βˆ’ 𝑓 (π‘₯). Reply: ____________________ Step three. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’1 βˆ’ 𝑓 (π‘₯). Reply: ____________________ Step four. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’1 + 𝑓 (π‘₯). Reply: ____________________ three. Use the graph to seek out the indicated limits. Step 1. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’1 βˆ’ 𝑓 (π‘₯). Reply: ____________________ Step 2. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’1 + 𝑓 (π‘₯). Reply: ____________________ Step three. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’1 𝑓 (π‘₯). Reply: ____________________ four. Discover the restrict algebraically by factoring the expression first. π’π’Šπ’Ž π‘₯ β†’ 2 ( 4π‘₯ 2 βˆ’ 3π‘₯ βˆ’ 10 π‘₯ βˆ’ 2 ) Reply: ____________________ 5. Take into account the graph of 𝑓 (π‘₯). What's the common charge of change of 𝑓 (π‘₯) from π‘₯1 = four to π‘₯2 = 7? Please write your reply as an integer or simplified fraction. Reply: ____________________ 6. 𝑓(π‘₯) is the rate in meters per hour a snowmobile is touring at π‘₯ hours. Which of the next does the slope 𝑓 β€² (π‘₯) symbolize? A) Route the snowmobile is touring at x hours. B) Common charge of change within the velocity of the snowmobile in meters per hour at x hours. C) Distance in meters the snowmobile has traveled in x hours. D) Charge of change of the rate of the snowmobile at x hours. 7. Take into account the operate 𝑓(π‘₯) = 4π‘₯ three βˆ’ 2π‘₯ 2 βˆ’ π‘₯ + eight. Step 1. Interpret the which means of 𝑓(1) = 9. A) The typical charge of change from π‘₯ = zero to π‘₯ = 1 is 9. B) The slope of the tangent line at π‘₯ = 1 is 9. C) The slope of the secant line from 𝑓(βˆ’1) to 𝑓(1) is 9. D) The worth of the operate evaluated at π‘₯ = 1 is 9. Step 2. Interpret the which means of 𝑓 β€² (1) = 7. A) The slope of the curve at π‘₯ = 1 is 7. B) The typical charge of change from π‘₯ = βˆ’1 to π‘₯ = 1 is 7. C) The peak of the operate at π‘₯ = 1 is 7. D) The typical charge of change from π‘₯ = zero to π‘₯ = 1 is 7. eight. Discover the by-product for the next operate. 𝑦 = βˆ’π‘₯ three 7 Reply: ____________________ 9. Discover the by-product for 𝑔(π‘₯) = 5π‘₯ 2 + 2π‘₯ three Reply: ____________________ 10. Discover the by-product for 𝑓 (π‘₯) = 5π‘₯ three + three βˆ’ 2π‘₯ 5 Reply: ____________________ 11. Use algebraic methods to rewrite 𝑔(π‘₯) = (3π‘₯ + 5)(3π‘₯ + four) as a sum or distinction; then discover 𝑔 β€² (π‘₯). Reply: ____________________ 12. Use algebraic methods to rewrite 𝑔(π‘₯) = βˆ’3π‘₯ 6 + 4π‘₯ three π‘₯2 as a sum or distinction; then discover 𝑔 β€² (π‘₯). Reply: ____________________ 13. For the operate 𝑓 (π‘₯) = βˆ’7π‘₯ three βˆ’ 8π‘₯ 2 βˆ’ 3π‘₯, Step 1. Discover the slope of the tangent line at π‘₯ = βˆ’5. Reply: ____________________ Step 2. Discover the equation of the tangent line at π‘₯ = βˆ’5. Reply: ____________________ 14. A rock is falling. It's 𝑓 (π‘₯) = βˆ’16π‘₯ 2 + 410 toes off the bottom after π‘₯ seconds. Step 1. Discover the instantaneous charge of change of the rock's place at π‘₯ = 2 seconds. Reply: ____________________ Step 2. When will the rock be 394 toes off the bottom? Reply: ____________________ 15. For the operate 𝑓(π‘₯) = 2π‘₯ three + 3π‘₯ 2 βˆ’ 7π‘₯, discover the slope of the tangent line at π‘₯ = βˆ’three. Reply: π‘š =_______________ 16. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’9 βˆ’ (5π‘₯ 2 + 6) Reply: ____________________ 17. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’2 βˆ’ ( 18 βˆ’ π‘₯ βˆ’19π‘₯ + 2 ) Reply: ____________________ 18. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ +∞ ( 15π‘₯ 11π‘₯2 + 10) Reply: ____________________ 19. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’βˆž ( βˆ’5π‘₯ 2 βˆ’ three 2π‘₯2 + 9 ) Reply: ____________________ 20. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’βˆž ( π‘₯ three βˆ’ 27 π‘₯2 + 3π‘₯ + 9 ) Reply: ____________________ 21. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’three + (βˆ’18π‘₯ + 10 π‘₯ + three ) Reply: ____________________ 22. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ βˆ’9 (βˆšβˆ’10π‘₯ + 14 + 16) Reply: ____________________ 23. Discover the restrict. π’π’Šπ’Ž π‘₯ β†’ +∞ ( βˆ’3π‘₯ 2 + 16π‘₯ + four 5π‘₯3 + 4π‘₯2 + 2π‘₯ + 5 ) Reply: ____________________ 24. Take into account the operate 𝑓 (π‘₯) = { βˆ’four 𝑖𝑓π‘₯ < 2 7π‘₯ βˆ’ 18 𝑖𝑓π‘₯ β‰₯ 2 . Step 1. Discover π’π’Šπ’Ž π‘₯ β†’ 2 βˆ’ 𝑓 (π‘₯). Reply: ____________________ Step 2. Discover π’π’Šπ’Ž π‘₯ β†’ 2 + 𝑓 (π‘₯). Reply: ____________________ Step three. Discover π’π’Šπ’Ž π‘₯ β†’ 2 𝑓 (π‘₯). Reply: ____________________ 25. Use the graph of 𝑦 = 𝑓 (π‘₯) to reply the query concerning the operate. Step 1. Discover π’π’Šπ’Ž π‘₯ β†’ 1 βˆ’ 𝑓 (π‘₯). A) ____________ B) Does Not Exist Step 2. Discover π’π’Šπ’Ž π‘₯ β†’ 1 + 𝑓 (π‘₯). Reply: ____________________ Step three. Discover 𝑓 (1). Reply: ____________________ Step four. Is 𝑓 (π‘₯) steady at π‘₯ = 1? A) Sure B) No 26. Use the graph of 𝑦 = 𝑓 (π‘₯) to reply the query concerning the operate. Step 1. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’2 βˆ’ 𝑓 (π‘₯). A) ____________ B) Does Not Exist Step 2. Discover π’π’Šπ’Ž π‘₯ β†’ βˆ’2 + 𝑓 (π‘₯). Reply: ____________________ Step three. Discover 𝑓 (βˆ’2). Reply: ____________________ Step four. Is 𝑓 (π‘₯) steady at π‘₯ = βˆ’2? A) Sure B) No 27. Take into account the next operate: 𝑓 (π‘₯) = { 4π‘₯ 2 βˆ’ 9π‘₯ βˆ’ three 𝑖𝑓π‘₯ < βˆ’four 5π‘₯ 2 βˆ’ 6π‘₯ + 2 𝑖𝑓π‘₯ β‰₯ βˆ’four Step 1. At what π‘₯-value is the operate discontinuous? Reply: ____________________ Step 2. What kind of discontinuity is on the discontinuous level? A) Non-Detachable Discontinuity B) Detachable Discontinuity C) Soar Discontinuity 28. Use the Product Rule or Quotient Rule to seek out the by-product. 𝑓(π‘₯) = (βˆ’π‘₯ three βˆ’ 7)(βˆ’2π‘₯ βˆ’1 + 6) Reply: 𝑓 β€² (π‘₯) =_______________ 29. Use the Product Rule or Quotient Rule to seek out the by-product. 𝑓(π‘₯) = 8π‘₯ three + 16π‘₯ 2 βˆ’ 16π‘₯ βˆ’ 32 2π‘₯ + four Reply: 𝑓 β€² (π‘₯) =_______________ 30. Given 𝑓(βˆ’6) = βˆ’2, 𝑓 β€² (βˆ’6) = βˆ’18, 𝑔(βˆ’6) = βˆ’12, and 𝑔 β€² (βˆ’6) = 7, discover the worth of β„Ž β€² (βˆ’6) primarily based on the operate beneath. β„Ž(π‘₯) = 𝑓(π‘₯) 𝑔 (π‘₯) Reply: β„Ž β€² (βˆ’6) =_______________ 31. Use the Product Rule or Quotient Rule to seek out the by-product. 𝑓(π‘₯) = (3π‘₯ three + 9)(3π‘₯ four βˆ’ 1) Reply: 𝑓 β€² (π‘₯) =_______________ 32. Use the Product Rule or Quotient Rule to seek out the by-product. 𝑓(π‘₯) = 3π‘₯ 6 βˆ’ 2 4π‘₯3 βˆ’ 5 Reply: 𝑓 β€² (π‘₯) =_______________ 33. Discover the by-product for the given operate. Write your reply utilizing optimistic and destructive exponents as an alternative of fractions and use fractional exponents as an alternative of radicals. β„Ž(π‘₯) = (7π‘₯ four + 9) three Reply: ____________________ 34. Discover the by-product for the given operate. Write your reply utilizing optimistic and destructive exponents as an alternative of fractions and use fractional exponents as an alternative of radicals. 𝑓 (π‘₯) = ( π‘₯ four + four βˆ’9π‘₯2 + 10) three Reply: ____________________ 35. Take into account the operate. 𝑓 (π‘₯) = βˆ’π‘₯ 2 + 6π‘₯ βˆ’ 6 Step 1. Discover all values of π‘₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π‘₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 36. Take into account the operate. 𝑓 (π‘₯) = 3π‘₯ three βˆ’ 18π‘₯ 2 + 36π‘₯ βˆ’ 26 Step 1. Discover all values of π‘₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π‘₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 37. Take into account the operate. 𝑓 (π‘₯) = π‘₯ + 7 π‘₯ βˆ’ 1 Step 1. Discover all values of π‘₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π‘₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 38. Take into account the operate: 𝑓 (π‘₯) = three(βˆ’3π‘₯ 2 + 48) 2 + four Step 1. Discover the important values of the operate. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Check to seek out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 39. Take into account the operate: 𝑓 (π‘₯) = π‘₯ three βˆ’ 3π‘₯ 2 βˆ’ 24π‘₯ + four Step 1. Discover the important values of the operate. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Check to seek out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 40. Take into account the operate 𝑓 (π‘₯) = 4π‘₯ three βˆ’ 108π‘₯ on the interval [βˆ’4, 4]. Discover absolutely the extrema for the operate on the given interval. Specific your reply as an ordered pair (π‘₯, 𝑓 (π‘₯)). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 41. Take into account the operate 𝑓 (π‘₯) = 4π‘₯ three βˆ’ 12π‘₯ 2 βˆ’ 288π‘₯ on the interval [βˆ’7, 7]. Discover absolutely the extrema for the operate on the given interval. Specific your reply as an ordered pair (π‘₯, 𝑓 (π‘₯)). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 42. Take into account the operate: 𝑓 (π‘₯) = 7π‘₯ three βˆ’ 8π‘₯ 2 + 7π‘₯ Step 1. Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ Step 2. Consider 𝑓 β€²β€²(βˆ’5), 𝑓 β€²β€²(eight), and 𝑓 β€²β€²(6), in the event that they exist. If they don't exist, choose "Does Not Exist". A) 𝑓 β€³ (βˆ’5) =____________ B) 𝑓 β€³ (βˆ’5) Does Not Exist A) 𝑓 β€³ (eight) =____________ B) 𝑓 β€³ (eight) Does Not Exist A) 𝑓 β€³ (6) =____________ B) 𝑓 β€³ (6) Does Not Exist 43. Take into account the operate: 𝑓 (π‘₯) = 3π‘₯ 2 βˆ’ 6√π‘₯ four + eight Step 1. Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ Step 2. Consider 𝑓 β€²β€²(2), 𝑓 β€²β€²(eight), and 𝑓 β€²β€²(three), in the event that they exist. If they don't exist, choose "Does Not Exist". A) 𝑓 β€³ (2) =____________ B) 𝑓 β€³ (2) Does Not Exist A) 𝑓 β€³ (eight) =____________ B) 𝑓 β€³ (eight) Does Not Exist A) 𝑓 β€³ (three) =____________ B) 𝑓 β€³ (three) Does Not Exist 44. Take into account the operate: 𝑓 (π‘₯) = 5π‘₯ three βˆ’ π‘₯ 2 + 6π‘₯ βˆ’ 6 Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ 45. Take into account the operate: 𝑓 (π‘₯) = βˆ’4π‘₯ three βˆ’ 36π‘₯ 2 + 2π‘₯ + 9 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π‘₯, 𝑦)-pairs. A) Factors of Inflection: ____________ B) None 46. Take into account the operate: 𝑓 (π‘₯) = √5π‘₯ + 1 Step 1. Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ Step 2. Consider 𝑓 β€²β€²(three), 𝑓 β€²β€²(7), and 𝑓 β€²β€²(6), in the event that they exist. If they don't exist, choose "Does Not Exist". A) 𝑓 β€³ (three) =____________ B) 𝑓 β€³ (three) Does Not Exist A) 𝑓 β€³ (7) =____________ B) 𝑓 β€³ (7) Does Not Exist A) 𝑓 β€³ (6) =____________ B) 𝑓 β€³ (6) Does Not Exist 47. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. 𝑓 (π‘₯) = 6π‘₯ three + 81π‘₯ 2 + 360π‘₯ A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 48. Take into account the operate: 𝑓 (π‘₯) = βˆ’4π‘₯ three + 6π‘₯ 2 + 240π‘₯ βˆ’ 12 Step 1. Discover the second by-product of the given operate. Reply: ____________________ Step 2. Use the Second By-product Check to find any native most or minimal factors within the graph of the given operate. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 49. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. 𝑓 (π‘₯) = 2π‘₯ three + 6π‘₯ 2 βˆ’ 48π‘₯ + 18 A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 50. Take into account the operate: 𝑓 (π‘₯) = (2π‘₯ 2 + 11) 2 Step 1. Discover the second by-product of the given operate. Reply: ____________________ Step 2. Use the Second By-product Check to find any native most or minimal factors within the graph of the given operate. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 51. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. 𝑓(π‘₯) = π‘₯ four + 16π‘₯ three βˆ’ 7 A) Native maxima: No native maxima; Native minima: No native minima B) Native maxima: No native maxima; Native minima: (βˆ’12,zero) C) Native maxima: (βˆ’12, βˆ’6919); Native minima: No native minima D) Native maxima: No native maxima; Native minima: (βˆ’12, βˆ’6919) 52. Discover the next indefinite integral. ∫(βˆ’4π‘₯ 2 βˆ’ 6)𝑑π‘₯ Reply: ____________________ 53. Discover the next indefinite integral. ∫( βˆ’2 π‘₯ + 5π‘₯ βˆ’ four 5 + 8𝑒 π‘₯ )𝑑π‘₯ Reply: ____________________ 54. Discover the next indefinite integral. ∫(βˆ’2𝑒 π‘₯ βˆ’ 8π‘₯ βˆ’three + three 7 )𝑑π‘₯ Reply: ____________________ 55. Carry out the indicated multiplication after which combine. ∫π‘₯ three (2π‘₯ βˆ’ 9)𝑑π‘₯ Reply: ____________________ 56. Consider the particular integral beneath. three ∫ 1 βˆ’5 π‘₯3𝑑π‘₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 57. Consider the particular integral beneath. four ∫ three ( βˆ’6 π‘₯2 βˆ’ 6)𝑑π‘₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 58. Consider the particular integral beneath. 5 ∫ 1 (2 + 4𝑒 π‘₯ )𝑑π‘₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 59. Consider the next particular integral. Write the precise reply. Don't spherical. ∫ (π‘₯ 2 + 5π‘₯ βˆ’ 12)𝑑π‘₯ four 2 Reply: _______________ 60. Discover the next indefinite integral. ∫(𝑒 π‘₯ βˆ’ 5 6 )𝑑π‘₯ Reply: ____________________ 61. Discover the next indefinite integral. ∫( 1 2 π‘₯ 1 eight + 7)𝑑π‘₯ Reply: ____________________ 62. Discover the next indefinite integral. ∫(12𝑒 𝑑 + 3𝑑)𝑑𝑑 Reply: ____________________ 63. Discover the next indefinite integral. ∫(5π‘₯ 9 βˆ’ 6 π‘₯ + 1 π‘₯5 )𝑑π‘₯ Reply: ____________________ 64. Simplify the indicated quotient after which combine. ∫ βˆ’5π‘₯ 6 + π‘₯ 5 βˆ’ eight π‘₯6 𝑑π‘₯ Reply: ____________________ 65. Take into account the operate: 𝑓 (π‘₯) = βˆ’2π‘₯ three βˆ’ 5π‘₯ 2 βˆ’ 9π‘₯ + four Step 1. Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ Step 2. Consider 𝑓 β€²β€²(four), 𝑓 β€²β€²(βˆ’9), and 𝑓 β€²β€²(zero), in the event that they exist. If they don't exist, choose "Does Not Exist". A) 𝑓 β€³ (four) =____________ B) 𝑓 β€³ (four) Does Not Exist A) 𝑓 β€³ (βˆ’9) =____________ B) 𝑓 β€³ (βˆ’9) Does Not Exist A) 𝑓 β€³ (zero) =____________ B) 𝑓 β€³ (zero) Does Not Exist 66. Take into account the operate: 𝑓 (π‘₯) = 2π‘₯ + 5 βˆ’6π‘₯ βˆ’ eight Step 1. Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ Step 2. Consider 𝑓 β€²β€²(10), 𝑓 β€²β€²(7), and 𝑓 β€²β€²(βˆ’three), in the event that they exist. If they don't exist, choose "Does Not Exist". A) 𝑓 β€³ (10) =____________ B) 𝑓 β€³ (10) Does Not Exist A) 𝑓 β€³ (7) =____________ B) 𝑓 β€³ (7) Does Not Exist A) 𝑓 β€³ (βˆ’three) =____________ B) 𝑓 β€³ (βˆ’three) Does Not Exist 67. Take into account the operate: 𝑓 (π‘₯) = 5π‘₯ 2 βˆ’ √π‘₯ + 6 Discover 𝑓 β€²β€²(π‘₯). Reply: ____________________ 68. Take into account the operate: 𝑓 (π‘₯) = 9π‘₯ 2 + 8π‘₯ βˆ’ 10 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π‘₯, 𝑦)-pairs. A) Factors of Inflection: ____________ B) None 69. Take into account the operate: 𝑓 (π‘₯) = π‘₯ three + 72√π‘₯ βˆ’ 5 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π‘₯, 𝑦)-pairs. A) Factors of Inflection: ____________ B) None 1. Step 1.Appropriate Reply: 35, 35.9, 35.99, 35.999 Step 2.Appropriate Reply: 36 2. Step 1.Appropriate Reply: π’π’Šπ’Ž π‘₯ β†’ βˆ’three βˆ’ 𝑓 (π‘₯) = βˆ’1 Step 2.Appropriate Reply: π’π’Šπ’Ž π‘₯ β†’ 1 βˆ’ 𝑓 (π‘₯) = βˆ’1 Step three.Appropriate Reply: π’π’Šπ’Ž π‘₯ β†’ βˆ’1 βˆ’ 𝑓 (π‘₯) = eight Step four.Appropriate Reply: π’π’Šπ’Ž π‘₯ β†’ βˆ’1 + 𝑓 (π‘₯) = βˆ’2 three. Step 1.Appropriate Reply: βˆ’four Step 2.Appropriate Reply: 1 Step three.Appropriate Reply: Does Not Exist four. Appropriate Reply: 13 5. Appropriate Reply: 2 three 6. Appropriate Reply: Charge of change of the rate of the snowmobile at π‘₯ hours. 7. Step 1.Appropriate Reply: The worth of the operate evaluated at π‘₯ = 1 is 9. Step 2.Appropriate Reply: The slope of the curve at π‘₯ = 1 is 7. eight. Appropriate Reply: 𝑦 β€² = βˆ’ three 7 π‘₯ βˆ’ four 7 9. Appropriate Reply: 𝑔 β€² (π‘₯) = 10π‘₯ + 6π‘₯ 2 10. Appropriate Reply: 𝑓 β€² (π‘₯) = 15π‘₯ 2 βˆ’ 10π‘₯ four 11. Appropriate Reply: 𝑔 β€² (π‘₯) = 18π‘₯ + 27 12. Appropriate Reply: 𝑔 β€² (π‘₯) = βˆ’12π‘₯ three + four 13. Step 1.Appropriate Reply: The slope of the tangent line at π‘₯ = βˆ’5 is βˆ’448. Step 2.Appropriate Reply: 𝑦 = βˆ’448π‘₯ βˆ’ 1550 14. Step 1.Appropriate Reply: βˆ’64 Step 2.Appropriate Reply: 1 15. Appropriate Reply: π‘š = 29 16. Appropriate Reply: 411 17. Appropriate Reply: 1 2 18. Appropriate Reply: zero 19. Appropriate Reply: βˆ’5 2 20. Appropriate Reply: βˆ’βˆž 21. Appropriate Reply: +∞ 22. Appropriate Reply: √104 + 16 23. Appropriate Reply: zero 24. Step 1.Appropriate Reply: βˆ’four Step 2.Appropriate Reply: βˆ’four Step three.Appropriate Reply: βˆ’four 25. Step 1.Appropriate Reply: three Step 2.Appropriate Reply: 2 Step three.Appropriate Reply: three Step four.Appropriate Reply: No 26. Step 1.Appropriate Reply: βˆ’three Step 2.Appropriate Reply: βˆ’three Step three.Appropriate Reply: 1 Step four.Appropriate Reply: No 27. Step 1.Appropriate Reply: βˆ’four Step 2.Appropriate Reply: Soar Discontinuity 28. Appropriate Reply: 𝑓 β€² (π‘₯) = βˆ’18π‘₯ 2 + 4π‘₯ βˆ’ 14π‘₯ βˆ’2 29. Appropriate Reply: 𝑓 β€² (π‘₯) = 8π‘₯ 30. Appropriate Reply: β„Ž β€² (βˆ’6) = 115 72 31. Appropriate Reply: 𝑓 β€² (π‘₯) = 63π‘₯ 6 + 108π‘₯ three βˆ’ 9π‘₯ 2 32. Appropriate Reply: 𝑓 β€² (π‘₯) = 36π‘₯ eight βˆ’ 90π‘₯ 5 + 24π‘₯ 2 (4π‘₯3 βˆ’ 5) 2 33. Appropriate Reply: three(7π‘₯ four + 9) 2 (28π‘₯ three ) 34. Appropriate Reply: three ( π‘₯ four + four βˆ’9π‘₯ 2 + 10) 2 ( (βˆ’9π‘₯ 2 + 10)(4π‘₯ three) βˆ’(π‘₯ four + four)(βˆ’18π‘₯) (βˆ’9π‘₯ 2 + 10)2 ) 35. Step 1.Appropriate Reply: three Step 2.Appropriate Reply: Rising: (βˆ’βˆž, three), Lowering: (three, ∞) 36. Step 1.Appropriate Reply: 2 Step 2.Appropriate Reply: Rising: (βˆ’βˆž, ∞), Lowering: ΓΈ 37. Step 1.Appropriate Reply: None Step 2.Appropriate Reply: Rising: ΓΈ, Lowering: (βˆ’βˆž, 1), (1, ∞) 38. Step 1.Appropriate Reply: π‘₯ = βˆ’four, zero, four Step 2.Appropriate Reply: Native Maxima: (zero, 6916), Native Minima: (βˆ’four, four), (four, four) 39. Step 1.Appropriate Reply: π‘₯ = βˆ’2, four Step 2.Appropriate Reply: Native Maxima: (βˆ’2, 32), Native Minima: (four, βˆ’76) 40. Appropriate Reply: Absolute Most: (βˆ’three, 216) Absolute Minimal: (three, βˆ’216) 41. Appropriate Reply: Absolute Most: (βˆ’four, 704) Absolute Minimal: (6, βˆ’1296) 42. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 42π‘₯ βˆ’ 16 Step 2.Appropriate Reply: 𝑓 β€²β€²(βˆ’5) = βˆ’226, 𝑓 β€²β€²(eight) = 320, 𝑓 β€²β€²(6) = 236 43. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 6 + 9 eight π‘₯ βˆ’7 four Step 2.Appropriate Reply: 𝑓 β€²β€²(2) = 6 + 9 √2 four 32 , 𝑓 β€²β€²(eight) = 6 + 9 √eight four 512 , 𝑓 β€²β€²(three) = 6 + √three four eight 44. Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 30π‘₯ βˆ’ 2 45. Step 1.Appropriate Reply: Concave Up: (βˆ’βˆž, βˆ’three), Concave Down: (βˆ’three, ∞) Step 2.Appropriate Reply: Factors of Inflection: (βˆ’three, βˆ’213) 46. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = βˆ’ 25 four (5π‘₯ + 1) βˆ’three 2 Step 2.Appropriate Reply: 𝑓 β€²β€²(three) = βˆ’25 256, 𝑓 β€²β€²(7) = βˆ’25 864, 𝑓 β€²β€²(6) = βˆ’ 25√31 3844 47. Appropriate Reply: Native Maxima: (βˆ’5, βˆ’525), Native Minima: (βˆ’four, βˆ’528) 48. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = βˆ’24π‘₯ + 12 Step 2.Appropriate Reply: Native Maxima: (5, 838), Native Minima: (βˆ’four, βˆ’620) 49. Appropriate Reply: Native Maxima: (βˆ’four, 178), Native Minima: (2, βˆ’38) 50. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 48π‘₯ 2 + 88 Step 2.Appropriate Reply: Native Maxima: No Native Maxima, Native Minima: (zero, 121) 51. Appropriate Reply: Native maxima: No native maxima; Native minima: (βˆ’12, βˆ’6919) 52. Appropriate Reply: βˆ’ four three π‘₯ three βˆ’ 6π‘₯ + 𝐢 53. Appropriate Reply: βˆ’2 ln( βƒ’ π‘₯βƒ’ ) + 25π‘₯ 1 5 + 8𝑒 π‘₯ + 𝐢 54. Appropriate Reply: βˆ’2𝑒 π‘₯ + 4π‘₯ βˆ’2 + three 7 π‘₯ + 𝐢 55. Appropriate Reply: 2 5 π‘₯ 5 βˆ’ 9 four π‘₯ four + 𝐢 56. Appropriate Reply: βˆ’20 9 57. Appropriate Reply: βˆ’13 2 58. Appropriate Reply: eight + 4𝑒 5 βˆ’ 4𝑒 β‰ˆ 590.78 59. Appropriate Reply: 74 three 60. Appropriate Reply: 𝑒 π‘₯ βˆ’ 5 6 π‘₯ + 𝐢 61. Appropriate Reply: four 9 π‘₯ 9 eight + 7π‘₯ + 𝐢 62. Appropriate Reply: 12𝑒 𝑑 + three 2 𝑑 2 + 𝐢 63. Appropriate Reply: 1 2 π‘₯ 10 βˆ’ 6 ln( βƒ’ π‘₯βƒ’ ) βˆ’ 1 four π‘₯ βˆ’four + 𝐢 64. Appropriate Reply: βˆ’5π‘₯ + ln( βƒ’ π‘₯βƒ’ ) + eight 5 π‘₯ βˆ’5 + 𝐢 65. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = βˆ’12π‘₯ βˆ’ 10 Step 2.Appropriate Reply: 𝑓 β€²β€²(four) = βˆ’58, 𝑓 β€²β€²(βˆ’9) = 98, 𝑓 β€²β€²(zero) = βˆ’10 66. Step 1.Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 168(βˆ’6π‘₯ βˆ’ eight) βˆ’three Step 2.Appropriate Reply: 𝑓 β€²β€²(10) = βˆ’21 39304, 𝑓 β€²β€²(7) = βˆ’21 15625, 𝑓 β€²β€²(βˆ’three) = 21 125 67. Appropriate Reply: 𝑓 β€²β€²(π‘₯) = 10 + 1 four π‘₯ βˆ’three 2 68. Step 1.Appropriate Reply: Concave Up: (βˆ’βˆž, ∞), Concave Down: None Step 2.Appropriate Reply: Factors of Inflection: None 69. Step 1.Appropriate Reply: Concave Up: (√9 5 , ∞), Concave Down: (zero, √9 5 ) Step 2.Appropriate Reply: Factors of Inflection: (√9 5 , βˆ’5 + 75√three 5 )

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