Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Consider the family of functions defined by: f(x) = 13x² + cos(kx) for k>0 Note: Note k is lowercase (a) Determine the second-derivative of f. f"(x) = (b) Determine the minimum and maximum value of f"(x). Your answer will be in terms of k. Min value of f"(x): Max value of f"(x): (c) Determine if the following statements are true or false. (i) The maximum value of f"(x) will be positive for any positive value of k. ---Select--- ✓ (ii) There exists a positive value of k so that the minimum value of f"(x) is negative. --Select--- (d) Use the results of parts (b) and (c) to determine conditions on k so that the graph of f has no inflection points. Write your result as an inequality. Inequality: (e) Use the result of parts (b) and (c) to determine conditions on k so that the graph of f has infinitely many inflection points. Write your result as an inequality. Inequality:
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Transcribed Image Text:Consider the family of functions defined by: f(x) = 13x² + cos(kx) for k>0 Note: Note k is lowercase (a) Determine the second-derivative of f. f"(x) = (b) Determine the minimum and maximum value of f"(x). Your answer will be in terms of k. Min value of f"(x): Max value of f"(x): (c) Determine if the following statements are true or false. (i) The maximum value of f"(x) will be positive for any positive value of k. ---Select--- ✓ (ii) There exists a positive value of k so that the minimum value of f"(x) is negative. --Select--- (d) Use the results of parts (b) and (c) to determine conditions on k so that the graph of f has no inflection points. Write your result as an inequality. Inequality: (e) Use the result of parts (b) and (c) to determine conditions on k so that the graph of f has infinitely many inflection points. Write your result as an inequality. Inequality:
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