2. Determine from the given graph whether the function has any absolute extreme values on (a, b). Then explain how your answer is consistent with the extreme value theorem. y y f(x) C Determine whether the function has any absolute extreme values on (a, b). Choose the correct choice below. A. The function has an absolute maximum value at x =c but does not have an absolute minimum value on (a, b). B. The function has an absolute maximum value at x =c and an absolute minimum value at x =b on (a, b) C. The function has an absolute minimum value at x = b but does not have an absolute maximum value on (a, b) D. The function does not have any absolute extreme values on (a, b) Explain the results in terms of the extreme value theorem. A. Since the function f is continuous on a closed interval, f attains both an absolute maximum value and an absolute minimum value on its domain. B. Since the function f is not continuous and the domain of f is a closed interval, f may or may not have any absolute extreme values on its domain C. Since the function f is continuous and the domain of f is not a closed interval, f may or may not have any absolute extreme values on its domain. O D. Since the function f is not continuous and the domain of f is not a closed interval, f may or may not attain any absolute extreme values on its domain
2. Determine from the given graph whether the function has any absolute extreme values on (a, b). Then explain how your answer is consistent with the extreme value theorem. y y f(x) C Determine whether the function has any absolute extreme values on (a, b). Choose the correct choice below. A. The function has an absolute maximum value at x =c but does not have an absolute minimum value on (a, b). B. The function has an absolute maximum value at x =c and an absolute minimum value at x =b on (a, b) C. The function has an absolute minimum value at x = b but does not have an absolute maximum value on (a, b) D. The function does not have any absolute extreme values on (a, b) Explain the results in terms of the extreme value theorem. A. Since the function f is continuous on a closed interval, f attains both an absolute maximum value and an absolute minimum value on its domain. B. Since the function f is not continuous and the domain of f is a closed interval, f may or may not have any absolute extreme values on its domain C. Since the function f is continuous and the domain of f is not a closed interval, f may or may not have any absolute extreme values on its domain. O D. Since the function f is not continuous and the domain of f is not a closed interval, f may or may not attain any absolute extreme values on its domain
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Determine from the given graph whether the function has any absolute extreme values on (a, b). Then explain how your answer is consistent with the extreme value theorem.
y
y f(x)
C
Determine whether the function has any absolute extreme values on (a, b). Choose the correct choice below.
A. The function has an absolute maximum value at x =c but does not have an absolute minimum value on (a, b).
B. The function has an absolute maximum value at x =c and an absolute minimum value at x =b on (a, b)
C. The function has an absolute minimum value at x = b but does not have an absolute maximum value on (a, b)
D. The function does not have any absolute extreme values on (a, b)
Explain the results in terms of the extreme value theorem.
A. Since the function f is continuous on a closed interval, f attains both an absolute maximum value and an absolute minimum value on its domain.
B. Since the function f is not continuous and the domain of f is a closed interval, f may or may not have any absolute extreme values on its domain
C. Since the function f is continuous and the domain of f is not a closed interval, f may or may not have any absolute extreme values on its domain.
O D. Since the function f is not continuous and the domain of f is not a closed interval, f may or may not attain any absolute extreme values on its domain
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