# P11 - a parabola.where does it have the largest value 2 Why do you think the farmer does not get more and more fruit by planting more and more

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Project 11 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 ) 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 3 trees instead of 2? 1

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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
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Unformatted text preview: a parabola. ..where does it have the largest value)? 2 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. ..) 2. Examine the piecewise-deﬁned function below for various values of the num-bers 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 0? Do all of these choices make f ( x ) diﬀerentiable at 0? Determine the particular values of m and b that will make f ( x ) diﬀerentiable at 0. 3...
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## This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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P11 - a parabola.where does it have the largest value 2 Why do you think the farmer does not get more and more fruit by planting more and more

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