# P10 - trees(Don’t worry about right or wrong.just write...

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Project 10 MAC 2311 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 ) : 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 3 trees instead of 2 ? Is the total yield increasing or decreasing at each of p = 2 , p = 8 , and p = 12 ? About how many trees should the farmer plant to have the largest yield and about how much fruit would be produced (remember that you have a parabola. ..where does it have the largest value)? Why do you think the farmer does not get more and more fruit by planting more and more

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Unformatted text preview: trees? (Don’t worry about right or wrong. ..just write down one reason this might happen. ..) 2. Examine the piecewise-deﬁned function below for various values of the numbers m and b : f ( x ) = 4 x + x 2 x ≤ mx + b x > Graph f ( x ) below with the given choices of m and b . m = 1 and b = 1 m =-1 and b = 0 m = 1 and b = 0 What are ALL of the possible choices of m and b will make f ( x ) continuous at ? Do any choices of m and b make f ( x ) differentiable at ? Determine the particular values of m and b that will make f ( x ) differentiable at . 3. Suppose lim x → f ( x ) = L . Find g (0) where g ( x ) = xf ( x ) x 6 = 0 x = 0 What does this tell you about the graph of xf ( x ) in general for a function f ( x ) at x = 0 ?...
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## This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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P10 - trees(Don’t worry about right or wrong.just write...

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