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# lecture10 - Lecture 10 Maximum and Minimum Values Lecture...

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Unformatted text preview: Lecture 10: Maximum and Minimum Values May 21, 2009 Lecture 10: Maximum and Minimum Values Objectives 1 Find critical points. 2 Classify critical points as maximum, minimum or other possibilities 3 Solve optimization problems. 4 Find the extreme values of functions on compact sets. Lecture 10: Maximum and Minimum Values Local maximum and minimums A function f ( x , y ) has a local maximum at ( a , b ) if f ( x , y ) ≤ f ( a , b ) when ( x , y ) is near ( a , b ) A function f ( x , y ) has a local minimum at ( a , b ) if f ( x , y ) ≥ f ( a , b ) when ( x , y ) is near ( a , b ) Lecture 10: Maximum and Minimum Values Local maximum and minimums A function f ( x , y ) has a local maximum at ( a , b ) if f ( x , y ) ≤ f ( a , b ) when ( x , y ) is near ( a , b ) A function f ( x , y ) has a local minimum at ( a , b ) if f ( x , y ) ≥ f ( a , b ) when ( x , y ) is near ( a , b ) If f has a local maximum or minimum at ( a , b ), then f x ( a , b ) = f y ( a , b ) = 0. Lecture 10: Maximum and Minimum Values Local maximum and minimums A function f ( x , y ) has a local maximum at ( a , b ) if f ( x , y ) ≤ f ( a , b ) when ( x , y ) is near (...
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lecture10 - Lecture 10 Maximum and Minimum Values Lecture...

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