Question 1
Given the revenue and cost functions R(x) = 26x - 0.4x
2 and
![](data:image/png;base64, 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)
, where x is the daily production, find the rate of change of revenue with respect to time when
![](data:image/png;base64, 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)
and
◦ $72/day
◦ $156/day
◦ $161.6/day
◦ $112/day
Question 2
Given the revenue and cost functions R(x) = 32x - 0.4x
2 and
![](data:image/png;base64, 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)
, where x is the daily production, find the rate of change of profit with respect to time when
![](data:image/png;base64, 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)
and
◦ $122/day
◦ $90/day
◦ $126/day
◦ $120/day