Lecture28

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

This preview shows pages 1–6. Sign up to view the full content.

Maxima and Minima November 27 Lecture 28

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

View Full Document
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
Examples Find the point on the plane x y + z = 4 that is closest to the point (1 , 2 , 3) . Lecture 28 2

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

View Full Document
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
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

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.

## This document was uploaded on 10/26/2011 for the course FKP bmfp at UTEM Chile.

### Page1 / 12

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online