2224-Sec12_7-HWT

2224-Sec12_7-HWT - Math 2224 Multivariable CalcSec. 12.7:...

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: Math 2224 Multivariable CalcSec. 12.7: Extreme Values and Saddle Points I. Review from 1205 A. Definitions 1. Local Extreme Values (Relative) a. A function f has a local maximum value at an interior point c of its domain if f x ( ) ! f c ( ) for all x in an open interval containing c . b. A function f has a local minimum value at an interior point c of its domain if f x ( ) ! f c ( ) for all x in an open interval containing c . 2. Critical Number a. A critical number of a function f is a number c in the domain of f such that ! f ( c ) is zero or ! f ( c ) does not exist (undefined). (A stationary point exists where ! f ( x ) = and a singular point exists where ! f ( x ) is undefined.) b. If f has a local maximum or minimum at c , then c is a critical number of f . 3. A point where the graph of a function has a tangent line and where the concavity changes is called a point of inflection . B. The First Derivative Test for Local Extrema Let f be a continuous function on [ a,b ] and c be a critical number in [ a,b ]. 1. If ! f ( x ) " on ( a,c ) and ! f ( x ) " on ( c,b ), then f has a local maximum of f(c) at x=c . 2. If ! f ( x ) " on ( a,c ) and ! f ( x ) " on ( c,b ), then f has a local minimum of f(c) at x=c ....
View Full Document

This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

Page1 / 7

2224-Sec12_7-HWT - Math 2224 Multivariable CalcSec. 12.7:...

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