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Unformatted text preview: Maxima and Minima Lecture 28 March 5, 2007 Lecture 28 Maxima and Minima Second Derivative Test Fact Suppose the second partial derivatives of f are continuous on a disk with center ( a , b ) , and suppose that f x ( a , b ) = and f y ( a , b ) = . Let D = f xx f xy f yx f yy = f xx f yy ( f xy ) 2 . 1 If D > and f xx ( a , b ) > , then f ( a , b ) is a local minimum. 2 If D > and f xx ( a , b ) < , then f ( a , b ) is a local maximum. 3 If D < , then f ( a , b ) is not a local maximum or minimum. In this case the point ( a , b ) is called a saddle point of f . Lecture 28 Maxima and Minima Examples Examples Lecture 28 Maxima and Minima Examples Examples Find the point on the plane x y + z = 4 that is closest to the point ( 1 , 2 , 3 ) . Lecture 28 Maxima and Minima Examples Examples Find the point on the plane x y + z = 4 that is closest to the point ( 1 , 2 , 3 ) . Find the points on the surface x 2 y 2 z = 1 that are closest to the origin. Lecture 28 Maxima and Minima Examples Examples Find the point on the plane x y + z = 4 that is closest to the point ( 1 , 2 , 3 ) ....
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 Fall '11
 jayjohn
 Extreme value, absolute maximum

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