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Unformatted text preview: Lecture 20 — Optimization We have now learned two main techniques to find the absolute maxima and minima of functions that are PROVIDED to us. One is the strategy for con tinuous functions on closed, bounded intervals; we also can use graphical techniques to see the range of the function. In this lecture we must first apply modeling techniques to provide the function our selves, and then use calculus to find the extrema. This will NOT generally be on a closed, bounded interval. A simple technique that is often used in optimization problems is the following: If c is the only critical number of f and there is a relative extremum at c (the derivative changes sign at c ), then f ( c ) is an absolute extreme value. Example: f ( x ) = xe x on ( 0 , ∞ ) . Strategy for optimization problems: (1) Identify the quantity that is to be maximized or minimized. Assign some convenient symbol to represent it ( Q , for example)....
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This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus

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