{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture27

# Lecture27 - Maxima and Minima Lecture 28 March 5 2007...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ) ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 19

Lecture27 - Maxima and Minima Lecture 28 March 5 2007...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online