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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2(7 – x) 49. y = 2x³ = (x)f x² -x+て %3D (x – 1)4 51. y = 16x - %3D 2(2x + 1) 53. y = 3x4 4. f(x) = (x – 1)4 6(3x2 + 2) 55. y = 4x² 57. y = x'/ 59. y = 4x (x – 1)2if"(x) . %3D %3D | 5. f(x) %3D (x2 – 2)3 x(2x² – 3a?) %3D | = (x),,f:zx – zv^x = (x)f *9 (a² – x²)3/2 61. y = 2x %3D - %D %3D In Problems 7–34, determine concavity and the x-values where points of inflection occur. Do not sketch the graphs. 463. Sketch f(2) = 4, ƒ 7. y = -2x2 + 4x 9. y = 4x3 + 12x2 – 12x 11. y = ax + bx² + cx + d 8. y = -74x2 + 19x – 37 10. y = x³ – 6x² + 9x + 1 64. Sketch ƒ(4) = 4, f %3D - 12. y = x – 8x² – 6 9x2 + 2x 65. Sketch f(1) = 1,f | 13. y = 2x4 – 48x2 + 7x + 3 14. y = 66. Sketch f(1) = 1, b f(x) > 0 ar %3D 4. 2. odT.(2.1) 18 16. y = ec2 tu 15. y = 2x'/5 %3D %3D 7x² +x +5 17. y = 67. Dema %3D 9. 2. equation p 5. 18. y = --x 1. 2 1. | 68. Avera 2. 19. y = 20 1. X- 2 3 st. 4. - - - 4' - 3x + 17x + 43 10 1. 21. y = 7. x²+6x² +5x – 4 show that - 30 12 concave u x + 1 22. y = x6 - 3x4 23. y = 69. Speci x - 1 x² 25. y = may depe: 1. 24. y = 1 - x² we see tha the left pl there are f x2 +1 ax² 21x + 40 27. y = 6(x+3)2 %3D 9+x 28. y = 3(x² – 2)² 29. y = 5e %3D 30. y = e – e* 31. y = axe 32. y = xe 33. y = 2x 34. y = 3e ter? In Problems 35-62, determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; inflection points; symmetry; and those intercepts that can be obtained conveniently. Then sketch the graph. 35
Transcribed Image Text:2(7 – x) 49. y = 2x³ = (x)f x² -x+て %3D (x – 1)4 51. y = 16x - %3D 2(2x + 1) 53. y = 3x4 4. f(x) = (x – 1)4 6(3x2 + 2) 55. y = 4x² 57. y = x'/ 59. y = 4x (x – 1)2if"(x) . %3D %3D | 5. f(x) %3D (x2 – 2)3 x(2x² – 3a?) %3D | = (x),,f:zx – zv^x = (x)f *9 (a² – x²)3/2 61. y = 2x %3D - %D %3D In Problems 7–34, determine concavity and the x-values where points of inflection occur. Do not sketch the graphs. 463. Sketch f(2) = 4, ƒ 7. y = -2x2 + 4x 9. y = 4x3 + 12x2 – 12x 11. y = ax + bx² + cx + d 8. y = -74x2 + 19x – 37 10. y = x³ – 6x² + 9x + 1 64. Sketch ƒ(4) = 4, f %3D - 12. y = x – 8x² – 6 9x2 + 2x 65. Sketch f(1) = 1,f | 13. y = 2x4 – 48x2 + 7x + 3 14. y = 66. Sketch f(1) = 1, b f(x) > 0 ar %3D 4. 2. odT.(2.1) 18 16. y = ec2 tu 15. y = 2x'/5 %3D %3D 7x² +x +5 17. y = 67. Dema %3D 9. 2. equation p 5. 18. y = --x 1. 2 1. | 68. Avera 2. 19. y = 20 1. X- 2 3 st. 4. - - - 4' - 3x + 17x + 43 10 1. 21. y = 7. x²+6x² +5x – 4 show that - 30 12 concave u x + 1 22. y = x6 - 3x4 23. y = 69. Speci x - 1 x² 25. y = may depe: 1. 24. y = 1 - x² we see tha the left pl there are f x2 +1 ax² 21x + 40 27. y = 6(x+3)2 %3D 9+x 28. y = 3(x² – 2)² 29. y = 5e %3D 30. y = e – e* 31. y = axe 32. y = xe 33. y = 2x 34. y = 3e ter? In Problems 35-62, determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; inflection points; symmetry; and those intercepts that can be obtained conveniently. Then sketch the graph. 35
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