×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

MAT 211- Lecture 8

by: Brigette Maggio

72

0

4

MAT 211- Lecture 8 MAT 211

Marketplace > Arizona State University > Math > MAT 211 > MAT 211 Lecture 8
Brigette Maggio
ASU
GPA 3.9

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

These notes cover MAT 211- Lecture 8 on Extreme Value Theorem for Function of 2 Variables.
COURSE
PROF.
Dr. Mohacsy
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math, MAT 211
KARMA
25 ?

Popular in Math

This 4 page Class Notes was uploaded by Brigette Maggio on Friday January 29, 2016. The Class Notes belongs to MAT 211 at Arizona State University taught by Dr. Mohacsy in Fall 2015. Since its upload, it has received 72 views. For similar materials see Math for Business Analysis in Math at Arizona State University.

×

Reviews for MAT 211- Lecture 8

×

×

What is Karma?

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 01/29/16
MAT 211­ Lecture 8­ Extreme Value Theorem for Function of 2 Variables  ­If f is a continuous function of 2 variables whose domain D is both closed and bounded,  then, there are points (x1​ 1​and (x2​ 2​in D such that f has an absolute min. at (x1​ 1​and an  absolute max. at (x​ ,y).  2​ 2​     Ex. #1: z= f(x,y)= (x­4)​ + (y­2) +40  0< and =x< and = 10  0< and =x< and = 15  Find absolute extreme.  1.) Locate all the critical points.  Zx= 2(x­4) *1 2(x­4)=0 x=4  Zy= 2(y­2) * 1 2(y­2)=0 y=2    Look back to shaded graph problem from last lecture.    2.) Find the critical points along the boundaries. (candidates for absolute extrema)  Boundaries: y=0 y=15 x=0 x=10    Case 1: y=0  2​ 2​ z= f(x)= (x­4)​ + (0­2)​+ 40            = (x­4 + 44          z= 2(x­4)= 0 x=4  Critical Point along boundary= x=4 & y=0    Case 2: y=15  2​ 2​ z= f(x)= (x­4)​  + (15­2)​  +40            = (x­4)​+169 +40     (209)        Zx= 2(x­4) x=4  Critical Point along boundary x=4 & y=15    Case 3: x=0  2​ 2​ z= f(x)= (0­4)​  + (y­2)​ + 40            = (y­2 +56        Zy= 2(y­2) y=2  Critical Point along boundary x=0 & y=2    Case 4: x=10  2​ 2​ z= f(x)= (10­4)​ + (y­2)​ +40            = (y­2 +76        Zy= 2(y­2) y=2  Critical Point along boundary x=10 & y=2                                  3.) The end points are, also, candidates for absolute extrema.   (0,0) (10,0) (10, 15) (0,15)  Make a table and plug in points to get values of f.    fmax.= 245 at (10,15)  fmin.= 40 at (4, 2)    ­Ex. #2: f(x,y)= (x­4 + (y­26) + 430  0< and =x< and =20  0< and =y< and =10  Find absolute extrema.    1.) Find the critical points.  Zx= 2(x­4)= 0 x=4  Zy= 2(y­26)= 0 y=26 ­­­­­>NOT​  inside region. DNOT ​ test it!    2.) Find critical points along the boundary.  Boundaries: y=0  y=10 x=0 x=20      Case 1: y=0 z=(x­4)​ + (0­26) + 430  2​   = (x­4 + …            Zx= 2(x­4)=x=4 & y=0    Case 2: y=10  2​ 2​ z=(x­4)​ + (10­26) +430                = + (­16) + 430            Zx= 2(x­4)=x=4 & y=10    Case 3: x=0  z= (0­4) + (y­26) + 430           Zy= 2(y­26) y=26 & x=0  ­­­­­ NOT​ in domain. Do NOT​  test!    Case 4: x=20  2​ 2​ z= (20­4)​ + (y­26 + 430           Zy= 2(y­26) y=26 & x=20 ­­­­­> NOT​ in domain. Do ​OT​ test!

×

25 Karma

×

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made \$280 on my first study guide!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

Refund Policy

STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com