8. 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. y 4 sin x, 0
8. 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. y 4 sin x, 0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:8.
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.
y 4 sin x,
0 <x<2Tt
Sketch the graph of y 4 sinx. Choose the correct graph below.
O A.
Ос.
В.
D.
y
5-
57t
х
х
х
X
Determine whether the function has any absolute extreme values on its domain. Choose the correct option below and fill in the input boxes as needed.
(Type an exact answer, using n as needed.)
O A. The function has an absolute maximum value at x =
but does not have an absolute minimum value on its domain.
on its domain.
B. The function has an absolute maximum value at x=
and an absolute minimum value at x =
but does not have an absolute maximum value on its domain
C. The function has an absolute minimum value at x =
D. The function does not have any absolute extreme values on its domain.
Explain the results in terms of the extreme value theorem.
O A. Since the function f is continuous on an open interval, it may or may not have any absolute extreme values on its domain.
B. Since the function f is not continuous on an open interval, it does not attain any absolute extreme values on its domain
C. Since the function f is not continuous on a closed interval, it may or may not have any absolute extreme values on its domain.
D. Since the function f is continuous on a closed interval, it attains both an absolute maximum value and an absolute minimum value on its domain.
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