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Unformatted text preview: Lecture 28 (Chapter 4, Section 28): Optimization Problems ex. Find two nonnegative numbers so that the prod uct of the flrst and the square of the second is a max imum, if the sum of the flrst and 4 times the second is 600. 2 To Solve an Optimization Problem 1. Read the problem carefully to determine the quan tity Q that you are trying to optimize, and the conditions involved. 2. Draw a sketch if possible and assign symbols to known and unknown quantities. 3. Find the function representing the quantity to be optimized ( Q ): the Primary Function 4. Find an equation relating the variables involved (the Constraint ) and write the primary function as the function of a single variable. 5. Use calculus to flnd the desired maximum or min imum; check your result. 3 ex. A closed rectangular box is to be constructed with a surface area of 48 square feet so that its length is twice the width. What dimensions will maximize the volume of the box? What is the maximum vol ume? 4 First Derivative Test for Absolute Extreme Values Let c be a critical number of a continuous function...
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 Spring '08
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 Calculus, Geometry

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