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. Лу 10- y = f(x) ol C1 C2 a Determine whether the function has any absolute extreme values on [a, b]. Choose the correct choice below. O 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= c2 and an absolute minimum value at x =b on [a, b]. C. The function does not have any absolute extreme values on [a, b]. D. The function has an absolute minimum value x = b but does not have an absolute maximum value 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 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 C. 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. D. 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.
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. Лу 10- y = f(x) ol C1 C2 a Determine whether the function has any absolute extreme values on [a, b]. Choose the correct choice below. O 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= c2 and an absolute minimum value at x =b on [a, b]. C. The function does not have any absolute extreme values on [a, b]. D. The function has an absolute minimum value x = b but does not have an absolute maximum value 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 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 C. 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. D. 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.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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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.
Лу
10-
y = f(x)
ol
C1 C2
a
Determine whether the function has any absolute extreme values on [a, b]. Choose the correct choice below.
O 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= c2 and an absolute minimum value at x =b on [a, b].
C. The function does not have any absolute extreme values on [a, b].
D. The function has an absolute minimum value x = b but does not have an absolute maximum value 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 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 C. 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.
D. 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6d9eff-5005-449d-8fe7-850b09d3d5bf%2F5298b88c-05b1-4152-91ed-0d637104f50b%2Fjoz3qxi.png&w=3840&q=75)
Transcribed Image Text: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.
Лу
10-
y = f(x)
ol
C1 C2
a
Determine whether the function has any absolute extreme values on [a, b]. Choose the correct choice below.
O 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= c2 and an absolute minimum value at x =b on [a, b].
C. The function does not have any absolute extreme values on [a, b].
D. The function has an absolute minimum value x = b but does not have an absolute maximum value 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 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 C. 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.
D. 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.
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