Question 1182599: The following equation models the rate at which a worker produces so many units after x hours when the worker starts at 8AM. (Assume 8AM means x=0)
f(x)=-2x^2+8x+50
At what time is the worker working most efficiently and how many units is the worker producing at this time?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source):
Answer by MathTherapy(10557)  (Show Source):
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The following equation models the rate at which a worker produces so many units after x hours when the worker starts at 8AM. (Assume 8AM means x=0)
f(x)=-2x^2+8x+50
At what time is the worker working most efficiently and how many units is the worker producing at this time?
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change, and learn to do mathematics the right way.
With x being time, the worker works most efficiently when he/she puts in the number of hours that produces the maximum number
of units. Those maximum units occur when time, or 
From equation  , we then get: 
Now, with maximum units produced when x = 2 hours, we get maximum units of 
AS [x, f(x)], or (x, y) is (2, 58), time when he/she works most efficiently is: 8:00 a.m. + 2 hours = 10:00 a.m.
At 10:00 a.m., he/she will have produced maximum units of 58.
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