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B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a 0, then f has a global minimum. E. An extreme value occurs at the point (h, k). F. If a > 0, then f has a global maximum. G. None of the above Next we use some calculus to develop familiar ideas from a different perspective. To start, treat a, h, and k as constants and c - Find a critical value of f. (This will depend on at least one of a, h, and k.) Critical value = Assume that a < 0. Make a derivative sign chart for f. Based on this information, classify the critical value of f as a maximur OA. maximum OB. minimum OC. neither

B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a 0, then f has a global minimum. E. An extreme value occurs at the point (h, k). F. If a > 0, then f has a global maximum. G. None of the above Next we use some calculus to develop familiar ideas from a different perspective. To start, treat a, h, and k as constants and c - Find a critical value of f. (This will depend on at least one of a, h, and k.) Critical value = Assume that a < 0. Make a derivative sign chart for f. Based on this information, classify the critical value of f as a maximur OA. maximum OB. minimum OC. neither

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 32E
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Let a, h, and k be arbitrary real numbers with a 0, and let f be the function given by the rule f(x) = a(z - h)² + k. Which of the following statements are true about f? Select all that apply. A. The graph of y = f(x) is a line. B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a > 0, then f has a global minimum. E. An extreme value occurs at the point (h, k). OF. If a > 0, then f has a global maximum. G. None of the above Next we use some calculus to develop familiar ideas from a different perspective. To start, treat a, h, and k as constants and compute f'(x). f'(x) = Find a critical value of f. (This will depend on at least one of a, h, and k.) Critical value = Assume that a < 0. Make a derivative sign chart for f. Based on this information, classify the critical value of f as a maximum or minimum. OA. maximum B. minimum OC. neither
Transcribed Image Text:Let a, h, and k be arbitrary real numbers with a 0, and let f be the function given by the rule f(x) = a(z - h)² + k. Which of the following statements are true about f? Select all that apply. A. The graph of y = f(x) is a line. B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a > 0, then f has a global minimum. E. An extreme value occurs at the point (h, k). OF. If a > 0, then f has a global maximum. G. None of the above Next we use some calculus to develop familiar ideas from a different perspective. To start, treat a, h, and k as constants and compute f'(x). f'(x) = Find a critical value of f. (This will depend on at least one of a, h, and k.) Critical value = Assume that a < 0. Make a derivative sign chart for f. Based on this information, classify the critical value of f as a maximum or minimum. OA. maximum B. minimum OC. neither
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