An efficient study of the morning shift at a factory indicates that an average worker who starts at 8:00 AM will have produced Q(t) = -t^3 + 9t^2 +12t units t hours later. At what time during the morning is the worker performing most efficiently?
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Q(t) = -t^3 + 9t^2 +12t
Q'(t) = -3t^2 + 18t +12
-3t^2 + 18t +12 = 0
-6t + 18 = 0
t = 3
Time: 8:00 AM + 3 hrs = 11:00 AM
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Q'(t) = -3t^2 + 18t +12
-3t^2 + 18t +12 = 0
-6t + 18 = 0
t = 3
Time: 8:00 AM + 3 hrs = 11:00 AM
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