Lecture28 - Maxima and Minima November 27 Lecture 28 Second...

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Maxima and Minima November 27 Lecture 28
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Second Derivative Test Suppose the second partial derivatives of f are continuous on a disk with center ( a,b ) , and suppose that f x ( a,b ) = 0 and f y ( a,b ) = 0 . Let D = f xx f xy f yx f yy = f xx f yy ( f xy ) 2 . 1. If D > 0 and f xx ( a,b ) > 0 , then f ( a,b ) is a local minimum. 2. If D > 0 and f xx ( a,b ) < 0 , then f ( a,b ) is a local maximum. 3. If D < 0 , 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 1
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Examples Find the point on the plane x y + z = 4 that is closest to the point (1 , 2 , 3) . Lecture 28 2
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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 2
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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
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Lecture28 - Maxima and Minima November 27 Lecture 28 Second...

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