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Asked Oct 16, 2019
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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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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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Expert Answer

Step 1

Given information:

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The given function is y = 4 sinx, 0<x<27.

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Step 2

Sketch the graph of the function as follows.

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y=4sinx 3m From above figure the correct option is A.

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Step 3

Determine whether the function has any abs...

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y 4 sinx d (4 sin x) y' dx 4 cosx Substitute critical point as follows, 4 cos.r 0 cosx 0 37 2 2 Show Steps Check the sign off(x) = 4cos (x) at each monotone interval Summary of the monotone intervals behavior <x<2 0<x< 0 Increasing Increasing Maximum Decreasing Minimum Substitute x in y 4 sinx y 4 sin 4(1) =4 Thus, maximum at irles

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