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

Class Note for MATH 1314 at UH 2


Class Note for MATH 1314 at UH 2

Marketplace > University of Houston > Class Note for MATH 1314 at UH 2

No professor available

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

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

No professor available
Class Notes
25 ?




Popular in Course

Popular in Department

This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

Similar to Course at UH


Reviews for Class Note for MATH 1314 at UH 2


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: 02/06/15
M1314 Lesson 13 1 Math 1314 Lesson 13 Absolute Extrema In earlier sections you learned how to find relative local extrema These points were the high points and low points relative to the other points around them In this section you will learn how to find absolute extrema that is the highest high andor the lowest low on the domain of the function or on a specific closed interval Absolute Extrema on the Domain of f Definition If fx 5 fc for all xin the domain of I then fc is called the absolute maximum value of f If fx 2 fc for all x in the domain of I then fc is called the absolute minimum value of f Sometimes you will be asked to find the absolute extrema over the interval 0000 Example 1 State the absolute maximum andor absolute minimum values v 141950105111 Mn X30 90 0 Abso uki YVYtrx 050 79277757574737271 1234557291 M1314 Lesson 13 2 Example 2 State the absolute maximum andor absolute minimum values AbSOlq LQ Xvyz 46 22 1019501th MM is 2 As you can see from these two examples the absolute extrema may or may not exist To find absolute extrema on oooo or on the entire domain of the given function algebraically you must graph the function using the guide to curve sketching Absolute Extrema on a Closed Interval More often you will be asked to find the absolute extrema over a closed interval a b and for a continuous function those will always exist and they are much easier to find Theorem If a function fis continuous on a closed interval a b then fhas both an absolute maximum value and an absolute minimum value on a b M1314 Lesson 13 3 Finding the Absolute Extrema of fon a Closed Interval 1 Find the critical points of fthat lie in a b 2 Compute the value of the function at every critical point found in step 1 and also compute 1a and Kb 3 The absolute maximum value will be the largest value found in step 2 and the absolute minimum value will be the smallest value found in step 2 Note The absolute maximum value or the absolute minimum value refers to the yvalue of the point on the graph or t Read the question carefully 2 Example 3 Find the absolute extrema of fx x on the interval 1 3 F x72x 0 2x20 gtO tes gtlt J XoXT 3 Flt lt7 0 021 423 032 0 43 cz q meme max is 1 bolu klt Min is 0 Example 4 Find the absolute extrema of fx x3 3x2 1 on the interval 2 2 CDPltx73gtltLCagtlt 0 Absoh x Max 3951 3XCXZUO A bsoh rL m7 5quot 3x10 XZO x20 xL Eest gtltzfgtltogtlt2 4307 6233136014 2393 439 o CO33sz 40 2 5Lquotlr 32 c M1314 Lesson 13 4 Example 5 Find the absolute maximum value and the absolute minimum value of the function fx x2 2x over the interval 3 1 5900quot 2X4zo Absolu e maxf53 axt39z absolu e Min 5 X734 Q X393 X 1K 1 40337 3 zC337 q quot3 Cagtrc 3l260quot32 Cm 0 107 39z3 Example 6 Find the absolute maximum value and the absolute minimum value of the function fx 3x4 4x3 on the interval 1 2 a 4300 IZX3 080 Ab56QSltZMQX l5 1 ZXI CX D 0 Absehu cz mm 13quot 12x1 0 xo Xfo X x XOxxz 3 47 44 300 HQ D 3 5r p o 3 gt 39 Meg s at 07 3C0 LGC03 39 0 413 32 i 42 3 Ll quot 31 Example 7 Find the xcoordinate of the absolute extrema of 2 the fundio f0 3x5 2x on the interval 1 1 F x3lt3XFV339Z xz I XODX 4 z 0 VCD 360quot 26 x 9 Z Z E 3 2773S Ida E21 725 Y3 7 35 39ZHD39Q ch is und ww Z gtltYB 3 I rZlt l attxjjzst X Absoh ct max is 5 Wm JAI VotlkAQ AbSGlm CQ mlh 15 O M1314 Lesson 13 5 Example 8 An apartment complex has 100 onebedroom apartment units Research shows that the monthly profit in dollars realized from renting out x apartments is given by Px 12x2 2256x 48000 How many units should be rented out to maximize the monthly profit What is that monthly profit 39 loo PIX 24gtlt 2zSa to gt 2125 qt 2 Test X70 X3qul X ioo 48 000 1 12390 48000 r LII Ecaqi zzsquKD qxlouo 53032 PCroo 391 l ojL39l39ZZSVCldovtrglooo 57000 maximum PWO39FIL is oi 59032 q apartments ranted Example 9 A company that produces digital cameras wants to minimize its production costs They estimate that their total monthly cost for producing the camera is given by Cx 00025x2 80x 10000 Find the average cost function Find the level of production that results in the smallest test to verify that you have found a minimum cost I my 3 C04 2 OOZSKZJ w 41 oozsx ol lwox D x K v 39 39 393 C39Cx I 2 J IO3929o Cquot OIOUO ZX XL Q 3 ooz 194 zopwx X T X1 942 C f2 3 39 oo 2 1 OOOCZIOGQ x1 llo 70 gel a I l K zlmo C lCZmoo M 395 20360 2089 From this section you should be able to T lt0 Identify absolute extrema on 00 00 from a graph of 2 max Find absolute extrema on 5 b algebraically Solve word problems having to do with absolute extrema C 2 3067 2 5S0 CeS l P2r um H


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

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."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

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."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

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.