# hw helo - d xn dx = nxn 1 The derivative of tn is ntn-1 and...

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d x n   dx = nx n - 1

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The derivative of t n  is nt n-1  and the derivative of a sum is the sum of the derivatives. The yield, Y, of an apple orchard (measured in bushels of apples per acre) is a function of the  amount x of fertilizer in pounds used per acre. Suppose Y = f(x) = 320 +  130 x - 10x 2 . a) What is the yield if 5 pounds of fertilizer is used per acre? Ans:  720 b) Find f  (5). Ans:  30  (What are its units?) c) Should the manager use more than 5 pounds of fertilizer per acre, or less? Ans:  more   (answers: more, less) Explain. Feedback: a) Y = f(5) =  720 . b) f  (x) =  130  - 20x. So, f  (5) =  30  (Units = (bushels per acre)/(pounds of fertilizer per acre) = bushels per pound of fertilizer). c) More, because the rate of change of the yield (bushels per pound of fertilizer) is positive ( 30 ). So,  a little more fertilizer will improve the yield.
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## This note was uploaded on 04/16/2008 for the course MATH 127 taught by Professor Rudvalis during the Fall '07 term at UMass (Amherst).

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hw helo - d xn dx = nxn 1 The derivative of tn is ntn-1 and...

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