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63-76. Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. 63. f(x) = x² – 2x³ +1 - 64. fƒ(x) = −x² – 2x³ + 12x² 65. f(x) = 5x4 - 20x³ + 10 1 66. f(x) 1+x² 67. f(x) = e(x − 3) 68. f(x) = 2x² In x - 5x² 69. g(t) = ln (3t² + 1) 70. g(x)=√x -4 71. f(x) = e-x²/2 72. p(x) = x¹e +x 73. f(x)=√x ln x 74. h(t) = 2 + cos 2t on [0, π] 75. g(t) = 3t5 - 30t4 + 80t³ + 100 76. f(x) = 2x¹ + 8x³ + 12x²-x-2 =

63-76. Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. 63. f(x) = x² – 2x³ +1 - 64. fƒ(x) = −x² – 2x³ + 12x² 65. f(x) = 5x4 - 20x³ + 10 1 66. f(x) 1+x² 67. f(x) = e(x − 3) 68. f(x) = 2x² In x - 5x² 69. g(t) = ln (3t² + 1) 70. g(x)=√x -4 71. f(x) = e-x²/2 72. p(x) = x¹e +x 73. f(x)=√x ln x 74. h(t) = 2 + cos 2t on [0, π] 75. g(t) = 3t5 - 30t4 + 80t³ + 100 76. f(x) = 2x¹ + 8x³ + 12x²-x-2 =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 69 and 75? Show work, thank you! Answers are given.
inflection points at x = 65. Concave up on (-∞, 0), (2, ∞); concave down on (0, 2); inflection points at x = 0 and x = = 2 67. Concave down on (-∞, 1); concave up on (1, ∞); inflection point at x = 1 69. Concave up on (-1/√3, 1/√√3); concave down on - (-∞, -1/√√3), (1/√3, ∞o); inflection points at t = ±1/√3 71. Concave up on (-∞, -1), (1, ∞); concave down on (-1, 1); inflection points at x = ±1 = 73. Concave up on (0, 1); concave down on (1, 0); inflection point at x = 1 75. 77. X = = 2 Concave up on (0, 2), (4, ∞); concave down on (-∞, 0), (2, 4); inflection points at x = 0, 2, 4 Critical pts. x = 0 and x = 2; local max at x = 0, local min at 79. 81. 83. x = 1 85. Critical pt. x : 0 and x = 0; local max at x = 0 Critical pt. x = 6; local min at x = 6 Critical pts. x = 0 and x = = 1 Critical pts. x 0 and x = = = 1; local max at x = 0; local min at 2; local min at x = 0; local max at
Transcribed Image Text:inflection points at x = 65. Concave up on (-∞, 0), (2, ∞); concave down on (0, 2); inflection points at x = 0 and x = = 2 67. Concave down on (-∞, 1); concave up on (1, ∞); inflection point at x = 1 69. Concave up on (-1/√3, 1/√√3); concave down on - (-∞, -1/√√3), (1/√3, ∞o); inflection points at t = ±1/√3 71. Concave up on (-∞, -1), (1, ∞); concave down on (-1, 1); inflection points at x = ±1 = 73. Concave up on (0, 1); concave down on (1, 0); inflection point at x = 1 75. 77. X = = 2 Concave up on (0, 2), (4, ∞); concave down on (-∞, 0), (2, 4); inflection points at x = 0, 2, 4 Critical pts. x = 0 and x = 2; local max at x = 0, local min at 79. 81. 83. x = 1 85. Critical pt. x : 0 and x = 0; local max at x = 0 Critical pt. x = 6; local min at x = 6 Critical pts. x = 0 and x = = 1 Critical pts. x 0 and x = = = 1; local max at x = 0; local min at 2; local min at x = 0; local max at
63-76. Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. 63. f(x) = x² - 2x³ +1 64. f(x) = x² – 2x³ + 12x² 65. f(x) = 5x4 - 20x³ + 10 1 66. f(x) 1 + x² 67. f(x) = e(x − 3) 68. f(x) = 2x² ln x 69. g(t) = ln (3t² + 1) 70. g(x)=√x - 4 71. f(x) = e-x²/2 72.p(c) = *e® + 73. f(x)=√x ln x = 5x² 74. h(t) = 2 + cos 2t on [0, π] 75. g(t) = 3t5 – 30t4 + 80t³ + 100 76. f(x) = 2x4 + 8x³ + 12x² - x-2
Transcribed Image Text:63-76. Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. 63. f(x) = x² - 2x³ +1 64. f(x) = x² – 2x³ + 12x² 65. f(x) = 5x4 - 20x³ + 10 1 66. f(x) 1 + x² 67. f(x) = e(x − 3) 68. f(x) = 2x² ln x 69. g(t) = ln (3t² + 1) 70. g(x)=√x - 4 71. f(x) = e-x²/2 72.p(c) = *e® + 73. f(x)=√x ln x = 5x² 74. h(t) = 2 + cos 2t on [0, π] 75. g(t) = 3t5 – 30t4 + 80t³ + 100 76. f(x) = 2x4 + 8x³ + 12x² - x-2
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