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Sketch the graph of the following function and determine whether the function has any absolute extreme values on its domain. Explain how your answer is consistent with the extreme value theorem -2x, -1

Sketch the graph of the following function and determine whether the function has any absolute extreme values on its domain. Explain how your answer is consistent with the extreme value theorem -2x, -1

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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Sketch the graph of the following function and determine whether the function has any absolute extreme values on its domain. Explain how your answer is consistent with the extreme value theorem - 1<x<0 g(x)= - 2x, 2x+1, 0≤x≤1 O A. -2 -1- B. 2 -2 Determine whether the function has any absolute extreme values on its domain. Choose the correct answer below. 2 A. The function has an absolute maximum at x = 1 value but does not have an absolute minimum value on its domain. B. The function has an absolute minimum value at x = 0 and an absolute maximum at x = 1 on its domain. C. The function has an absolute minimum value at x = 0 but does not have an absolute maximum value on its domain. D. The function does not have any absolute extreme values on its domain. Explain the results in terms of the extreme value theorem. D. A. Since the function g is continuous on a closed interval, it attains both an absolute maximum value and an absolute minimum value on its domain. B. Since the function g is not continuous on a closed interval, it may or may not have any absolute extreme values on its domain. C. Since the function g is not continuous on an open interval, it does not attain any absolute extreme values on its domain. D. Since the function g is continuous on an open interval, it may or may not have any absolute extreme values on its domain. As
Transcribed Image Text:Sketch the graph of the following function and determine whether the function has any absolute extreme values on its domain. Explain how your answer is consistent with the extreme value theorem - 1<x<0 g(x)= - 2x, 2x+1, 0≤x≤1 O A. -2 -1- B. 2 -2 Determine whether the function has any absolute extreme values on its domain. Choose the correct answer below. 2 A. The function has an absolute maximum at x = 1 value but does not have an absolute minimum value on its domain. B. The function has an absolute minimum value at x = 0 and an absolute maximum at x = 1 on its domain. C. The function has an absolute minimum value at x = 0 but does not have an absolute maximum value on its domain. D. The function does not have any absolute extreme values on its domain. Explain the results in terms of the extreme value theorem. D. A. Since the function g is continuous on a closed interval, it attains both an absolute maximum value and an absolute minimum value on its domain. B. Since the function g is not continuous on a closed interval, it may or may not have any absolute extreme values on its domain. C. Since the function g is not continuous on an open interval, it does not attain any absolute extreme values on its domain. D. Since the function g is continuous on an open interval, it may or may not have any absolute extreme values on its domain. As
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