mthsc206-fall-2010-notes-15.7

mthsc206-fall-2010-notes-15.7 - 15.7 Maximum and Minimum...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 15.7 Maximum and Minimum Values Definition 15.7.1 We say that f ( x,y ) has a relative (or local) maximum at ( x ,y ) if there is some open disk D r ( x ,y ) where f ( x ,y ) f ( x,y ) for all points ( x,y ) D r ( x ,y ) . We say that f ( x,y ) has a relative (or local) minimum at ( x ,y ) if there is some open disk D r ( x ,y ) where f ( x ,y ) f ( x,y ) for all points ( x,y ) D r ( x ,y ) . Definition 15.7.2 We say that f has an absolute maximum at ( x ,y ) if f ( x ,y ) f ( x,y ) for all ( x,y ) in the domain of f . We say that f has an absolute minimum at ( x ,y ) if f ( x ,y ) f ( x,y ) for all ( x,y ) in the domain of f . Question: Is every absolute extrema a relative extrema? Support your answer. Example 15.7.1 Let f ( x,y ) = 4- x 2- y 2 . Are there any local extrema? any absolute extrema? What is true of the tangent plane when there is a relative extrema?...
View Full Document

This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Fall '07 term at Clemson.

Page1 / 2

mthsc206-fall-2010-notes-15.7 - 15.7 Maximum and Minimum...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online