lecture11

# lecture11 - MATH 100 Lecture 11 Maxima/ Minima of functions...

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

2006 Fall MATH 100 Lecture 11 1 MATH 100 Lecture 11 Maxima/ Minima of functions of 2 variables () () ( ) () ( ) ( ) D y x y x f y x f y x f r y x C y x y x f y x f y x y x f , , , , if , at maxima absolute an have to said is , , , , , , s.t. , at centered circle if , at maxima relative a have to said is : Definition 0 0 0 0 0 0 0 0 0 0 0 0

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

View Full Document
2006 Fall MATH 100 Lecture 11 2 MATH 100 Lecture 11 Maxima/ Minima of functions of 2 variables ( ) () ( ) ( ) ( ) ( ) ( ) D y x y x f y x f y x r y x C y x y x f y x f y x , , , , : , at minimum Absolute , , , , , , : , at minimum Relative 0 0 0 0 0 0 0 0 0 0 extremum Absolute maximum minimum Absolute extremum Relative maximum minimum Relative Terms
2006 Fall MATH 100 Lecture 11 3 MATH 100 Lecture 11 Maxima/ Minima of functions of 2 variables Relative minima: A,D Absolute minimum: A Relative maximum: B Absolute maximum: D

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

View Full Document
2006 Fall MATH 100 Lecture 11 4 MATH 100 Lecture 11 Maxima/ Minima of functions of 2 variables Two Questions : Are there any relative or absolute extrema? If so, where are they located? Answer to the first question: Theorem: If f(x,y) is continuous on a closed and bounded set R , then f has both an absolute maximum and an absolute minimum on R
2006 Fall MATH 100 Lecture 11 5 MATH 100 Lecture 11 Maxima/ Minima of functions of 2 variables () 0 , , then , , at exist and if and , , at extrema relative a has f If : Theorem 0 0 0 0 0 0 0 0 = = y x f y x f y x f f y x y x y x Finding Relative Extrema: a necessary condition ( ) ( ) ( ) ( ) () ( ) 0 , ' 0 , ' then , , , Define : Proof 0 0 0 0 = = = = = = y x f y H y x f x G y x f y H y x f x G y x

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

View Full Document
2006 Fall MATH 100 Lecture 11 6 MATH 100
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

### Page1 / 18

lecture11 - MATH 100 Lecture 11 Maxima/ Minima of functions...

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

View Full Document
Ask a homework question - tutors are online