I would like help with the highlighted questions with work, please. The directions for 15 and 23 are "Find the critical numbers and use the First Derivative Test to find any local extrema." C for question 81 says "Discuss which of the two tests you found easier."

Section 4.4 . Assess Your fix) = 3x4 - 4x3 16. h(x) =x4+2x3-3 15. 17. /(x) = (5 - 2x)et 18. f (x) = (x - 8)ex 57. f (x) = x4 - 4x 20. f (x) = x-2ex 59. f (x) = 5x4 -x5 21. f(x) =x43 + x1/3 22. f (x ) = =x2/3 -x1/3 61. f(x) = 3x5 - 20x3 63. f (x ) =x2ex 21 84x) =x23(x2 - 4) 24. f (x) =x1/3(x2 -9) 65. f ( x) - tex In x 26. h(x) = In x 2 25 f(x) = x3 67. f(x) = 6x4/3 - 3x1/3 27. 8(x) = 1x2-1/ 28. f (x) = 1x2-41 69. f (x ) = x2/3 ( x2 - 8) N. f(0) = sin 0 - 2 cos0 30. f (x) = x+2sinx 71. f (x ) = x2 - Inx 73. f ( x ) = X In Problems 31-38, the distance s of an object from the origin at (1 + x2) 5/2 time + 2 0 (in seconds) is given. The motion is along a horizontal line 75. f (x ) = x2 VI -x2 with the positive direction to the right. fa) Determine the intervals during which the object moves 77. f ( x ) = sin2x to the right and the intervals during which it moves to 79. f (x) = x - 2sinx, OSX=2x the left. (h) When does the object reverse direction? 80. f (x) = 2cos? x - sin x, 05x = 2 (c) When is the velocity of the object increasing and when is it decreasing? "d Draw a figure to illustrate the motion of the object. In Problems 81-84, find the local extrema o it) Draw a figure to illustrate the velocity of the object. (a) Using the First Derivative Test. (b) Using the Second Derivative Test. 31. 5 = 12 - 2+ + 3 32. 5 = 212 + 81 - 7 (c) Discuss which of the two tests you fou 33. s = 213 + 612 - 181 + 1 34. 5 = 314 - 1613 + 2412 81. f (x) = -2x3 + 15x2 - 36x +7 35 . s = 21 - -, 1>0 36. s = 3V1 _ _ 82. f (x) = x3 + 10.x2 + 25x - 25 VT' 1 20 83. f (x) = (x-3)2ex 37. s = 2 sin(3t), 0=1= 3 2 JT 38. s = 3 cos(It), OSIs2 Applications and Extensions In Problems 39-54, (a) determine the intervals on which each function is concave up and on which it is concave down; In Problems 85-96, sketch the graph of a c b) find any points of inflection. the given properties. Answers will vary. 39. f(x ) = x2 - 2x + 5 40. f (x) =x2+4x -2 85. f is concave up on (-oo, oo), increa 41. fix) = x3 - 9x2 + 2 decreasing on (0, co), and f (0) = 1. 42. f(x) =x3 - 6x2+ 9x +1 86. f is concave up on (-oo, 0), concav 43. f(x) = x4 -4x3 + 10 44. f(x) = 3x4 -8x3 + 6x +1 decreasing on (-oo, 0), increasing of 45. f(x) = x2/3ex 46. f (x ) = x2/3e-x 87. f is concave down on (-co, 1), con In x In x decreasing on (-oo, 0), increasing o 47. f(x) = x 3 48. f(x) = VX 3 and f (1) = 2. 88. f is concave down on (-co, 0), con 49. f (x ) = x + - 50. f (x) = 2x2 1 x on (-00, co), and f (0) = 1 and f(1 51 . f(x ) = 3x 1/3 + 2 x 52. f (x) = x4/3 -8x1/3 89. f'(x) > 0ifx 0 if x > 0 and f(0) = 1. 53. f (x ) = 3-4 + 4 54. f(x) = (x -1)3/2 90. f'(x) > 0ifx 0 and f (0) = 1. I Problems 55-80: 91. f"(0) = 0; f'(0) = 0; f"(x) > 0 if (a) Find the local extrema of f. and f (0) = 1. 10) Determine the intervals on which f is concave up and on which it 92. f"(0) = 0; f'(x) > 0ifx #0; f" is concave down . f"(x) > 0 if x > 0 and f (0) = 1. (cj Find any points of inflection. 93. f'(0) = 0; f'(x) 0; f(0) =1