P15Ans - 1 2 4 10 Draw the sign of Y 00 along the...

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Project 15 MAC 2233 1. One model that is used for an agricultural yield Y bushels (in thousands) as a function of soil nitrogen level N points is Y ( N ) = N 1 + N 2 . Calculate Y 0 ( N ) and Y 00 ( N ) . Give the units for each. Y 0 ( N ) = 1 - N 2 (1 + N 2 ) 2 Y 00 ( N ) = 2 N ( N 2 - 3) (1 + N 2 ) 3 At what level N is the yield experiencing zero growth? when N = 1 At what level(s) N is the yield experiencing zero acceleration? negative acceleration? neg acceleration on ( 0 , 3 ) As time passes (to infinity), what does the yield approach? the limit is zero Try to sketch the curve for N > 0 by plotting points for N = 0
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Unformatted text preview: , 1 , 2 , 4 , 10 . Draw the sign of Y 00 along the continuous graph. At what levels is the yield slowing down? slowing down occurs when Y and Y 00 have opposite sign: increasing at slower rate (on ( 0 , 1 ) ) or decreasing but at a more positive rate (on ( √ 3 , ∞ ) ) Diminishing Returns: All else being equal, the added benefit from an additional unit of input will eventually decrease. What does this say in terms of the first and second derivative?...
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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