# P10 - 3 trees instead of 2 Is the total yield increasing or...

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Project 10 MAC 2233 1. A farmer keeps a small private orchard with apple trees. Suppose the total yield Y (number of healthy apples) is a function of the number of trees planted p given by Y ( p ) = 120 p - 7 p 2 . Graph Y ( p ) below. Use the definition of the derivative to find the general formula dY dp , and then evaluate it at p = 2 , p = 8 , and p = 12 . Include units. Illustrate the slopes you found above by drawing tangent lines on your graph. Based on your answer to Y 0 (2) , how many more fruit would you guess the farmer will produce by planting a third tree? What is the actual difference in the number of fruit produced by planting
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Unformatted text preview: 3 trees instead of 2 ? Is the total yield increasing or decreasing at each of p = 2 , p = 8 , and p = 12 ? What is the signiﬁcance of the p for which dY dp = 0 ? About how many trees should the farmer plant to have the largest yield and about how much fruit would be produced ? Why do you think the farmer does not get more and more fruit by planting more and more trees? (Don’t worry about right or wrong. ..just write down one reason this might happen. ..)...
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