t5(2)

# t5(2) - Methods of Calculus Final Exam Name MAC3233...

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Methods of Calculus Final Exam Name MAC3233 April 22, 1996 Instructions: This is a closed-book, closed-notes test. Do not write your answers on this paper, use separate answer sheets. No calculators are allowed to be used. To receive credit, you must show all work . For the optimization problems, you are required to show why your answer is a minimum or maximum. Some numerical answers may involve the function ln or the number e . You are not required to simplify your answers. 1. (10 pts.) Let Q denote the output produced by a ﬁrm. In the short run Q = Q ( x ) is a function of the number x of units of labor hired ( x is the variable input). The marginal product is the derivative Q 0 ( x ). For small values of x , marginal product often increases so that Q increases at an increasing rate. (This is because of the increased specialization among units of the labor force.) As x increases, however, the law of diminishing marginal returns says that marginal product will eventually start to decrease. When this happens,

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## This note was uploaded on 07/13/2011 for the course MAC 2233 taught by Professor Staff during the Spring '08 term at FAU.

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t5(2) - Methods of Calculus Final Exam Name MAC3233...

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