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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