SOLUTION: Please find an interval for the function y=-2sin3(x-pi/2)+2, where the average rate of change is 0. thanks!

Question 896522: Please find an interval for the function y=-2sin3(x-pi/2)+2, where the average rate of change is 0. thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please find an interval for the function y=-2sin3(x-pi/2)+2, where the average rate of change is 0. thanks!
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Note:: rate = slope
Note:: Slope is 0 for the sin when the angle is 0 or pi or 2pi etc.
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Solve::
3(x-pi/2) = 0
Ans: x = pi/2
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OR
3(x-pi/2) = pi
(x - pi/2) = pi/3
x = (pi/3)+(pi/2) = 5pi/6 = (5/6)pi
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Note:: That may not be what you are looking for.
As the angle passes from pi/4 to (3/4)pi the sum of the slopes is zero
Solve:: 3(x-pi/2) = pi/4
x-pi/2 = pi/12
x = pi/12 + pi/2
x = (14/24)pi
x = (7/12)pi
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And:
3(x-pi/2) = (3/4)pi
x-pi/2 = (1/4)pi
x = (1/4 + 1/2)pi
x = (3/4)pi
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Cheers,
Stan H.
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