1.05.4.Literacy - Growth Authors: Bill Davis, Horacio Porta...

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Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 1.05 Using the Tools LITERACY · L.1) Find the largest value of the product x y given that x and y are related by x + y = 4 . · L.2) Examine the derivative of f @ x D = x e - x 2 to give a reasonably good hand sketch of the curve y = f @ x D on the axes below. What are the maximum and minimum values f @ x D can have ? The two plotted points are on the curve. - 2 - 1 1 2 x - 0.4 - 0.2 0.2 0.4 0.6 0.8 1.0 y · L.3) Examine the derivative of f @ x D = x 2 - 2 Log @ x D 2 to give a reasonably good sketch of the curve y = f @ x D = x 2 - 2 Log @ x D 2 on the axes below. What is the minimum value f @ x D = x 2 - 2 Log @ x D 2 can have? The plotted point is on the curve. 0 1 2 3 4 x 1 2 3 4 y · L.4) Use calculus to explain: The biggest rectangle with a fixed perimeter is the square. · L.5) Given a positive number t , factor the derivative of f @ x D = x t e x with respect to x to explain why the curve
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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