New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

MAT 211- Lecture 8

by: Brigette Maggio

MAT 211- Lecture 8 MAT 211

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

Preview These Notes for FREE

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

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

These notes cover MAT 211- Lecture 8 on Extreme Value Theorem for Function of 2 Variables.
Math for Business Analysis
Dr. Mohacsy
Class Notes
Math, MAT 211
25 ?




Popular in Math for Business Analysis

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


Report this Material


What is Karma?


Karma is the currency of StudySoup.

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! 


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

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 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


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


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:

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

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.