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-2 (a) Find the possible points of inflection of f. (b) Create a number line to determine the intervals on which f is concave up or concave down. (c) Find the critical points of f and use the Second Deriva- tive Test, when possible, to determine the relative ex- -4 trema. 6. Given the graph of f', identify the concavity of f and its in- flection points. (d) Find the x values where f'(x) has a relative maximum or minimum. 19. f(x) = x - 2x+1 20. f(x) = -x - 5x +7 21. f(x) = x - x + 1 22. f(x) = 2x - 3x + 9x + 5 23. f(x) = + - 2x + 3 4 3 24. f(x) = -3x + 8x + 6x – 24x + 2 25. f(x) = x* - 4x + 6x – 4x+1

-2 (a) Find the possible points of inflection of f. (b) Create a number line to determine the intervals on which f is concave up or concave down. (c) Find the critical points of f and use the Second Deriva- tive Test, when possible, to determine the relative ex- -4 trema. 6. Given the graph of f', identify the concavity of f and its in- flection points. (d) Find the x values where f'(x) has a relative maximum or minimum. 19. f(x) = x - 2x+1 20. f(x) = -x - 5x +7 21. f(x) = x - x + 1 22. f(x) = 2x - 3x + 9x + 5 23. f(x) = + - 2x + 3 4 3 24. f(x) = -3x + 8x + 6x – 24x + 2 25. f(x) = x* - 4x + 6x – 4x+1

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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Exercises 3.4 Terms and Concepts 7. Given the graph of f, identify the concavity of f and its in- flection points. 1. Sketch a graph of a function f(x) that is concave up on (0, 1) and is concave down on (1, 2). 2. Sketch a graph of a function f(x) that is: -2 2 (a) Increasing, concave up on (0, 1), (b) increasing, concave down on (1, 2), (c) decreasing, concave down on (2, 3) and (d) increasing, concave down on (3, 4). In Exercises 8-18, a function f(x) is given. 3. Is is possible for a function to be increasing and concave down on (0, o0) with a horizontal asymptote of y = 1? If so, give a sketch of such a function. (a) Compute f"(x). (b) Graph f and f" on the same axes (using technology is permitted) and verify Theorem 28. 4. Is is possible for a function to be increasing and concave up on (0, o0) with a horizontal asymptote of y = 1? If so, give 8. f(x) = -7x + 3 9. f(x) — —4x* + 3х— 8 a sketch of such a function. 10. f(x) = 4x + 3x – 8 11. f(x) = x – 3x² + x – 1 Problems 12. f(x) = -x + x – 2x + 5 13. f(x) = cos x 14. f(x) = sin x 15. f(x) = tan x 5. Given the graph of f", identify the concavity of f and its in- flection points. 1 16. f(x) x2 +1 1 17. f(x) = 1 18. f(x) = x² 2 In Exercises 19–37, a function f(x) is given. 22 (a) Find the possible points of inflection of f. -2 (b) Create a number line to determine the intervals on which f is concave up or concave down. (c) Find the critical points of f and use the Second Deriva- tive Test, when possible, to determine the relative ex- trema. 6. Given the graph of f', identify the concavity of f and its in- flection points. (d) Find the x values where f'(x) has a relative maximum or minimum. 19. f(x) — х — 2х + 1 20. f(x) = -x² – 5x + 7 21. fх) — х — х+1 22. f(x) = 2x – 3x + 9x + 5 x* 23. f(x) = + - 2x + 3 4 3 24. f(x) = -3x* + 8x³ + 6x? – 24x + 2 25. f(x) = x* – 4x³ + 6x² – 4x + 1 176
Transcribed Image Text:Exercises 3.4 Terms and Concepts 7. Given the graph of f, identify the concavity of f and its in- flection points. 1. Sketch a graph of a function f(x) that is concave up on (0, 1) and is concave down on (1, 2). 2. Sketch a graph of a function f(x) that is: -2 2 (a) Increasing, concave up on (0, 1), (b) increasing, concave down on (1, 2), (c) decreasing, concave down on (2, 3) and (d) increasing, concave down on (3, 4). In Exercises 8-18, a function f(x) is given. 3. Is is possible for a function to be increasing and concave down on (0, o0) with a horizontal asymptote of y = 1? If so, give a sketch of such a function. (a) Compute f"(x). (b) Graph f and f" on the same axes (using technology is permitted) and verify Theorem 28. 4. Is is possible for a function to be increasing and concave up on (0, o0) with a horizontal asymptote of y = 1? If so, give 8. f(x) = -7x + 3 9. f(x) — —4x* + 3х— 8 a sketch of such a function. 10. f(x) = 4x + 3x – 8 11. f(x) = x – 3x² + x – 1 Problems 12. f(x) = -x + x – 2x + 5 13. f(x) = cos x 14. f(x) = sin x 15. f(x) = tan x 5. Given the graph of f", identify the concavity of f and its in- flection points. 1 16. f(x) x2 +1 1 17. f(x) = 1 18. f(x) = x² 2 In Exercises 19–37, a function f(x) is given. 22 (a) Find the possible points of inflection of f. -2 (b) Create a number line to determine the intervals on which f is concave up or concave down. (c) Find the critical points of f and use the Second Deriva- tive Test, when possible, to determine the relative ex- trema. 6. Given the graph of f', identify the concavity of f and its in- flection points. (d) Find the x values where f'(x) has a relative maximum or minimum. 19. f(x) — х — 2х + 1 20. f(x) = -x² – 5x + 7 21. fх) — х — х+1 22. f(x) = 2x – 3x + 9x + 5 x* 23. f(x) = + - 2x + 3 4 3 24. f(x) = -3x* + 8x³ + 6x? – 24x + 2 25. f(x) = x* – 4x³ + 6x² – 4x + 1 176
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