×

### Let's log you in.

or

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

×

### Create a StudySoup account

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

or

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

Already have a StudySoup account? Login here

## Week 7 of Lecture Notes

by: Monica Weisenbach

38

0

4

# Week 7 of Lecture Notes MATH127

Monica Weisenbach
UMass
GPA 3.819
Calculus I for Life and Social Science Majors
Thurlow Cook

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 :)

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

×
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

These notes cover minimums, maximums, revenue functions and logistic functions.
COURSE
Calculus I for Life and Social Science Majors
PROF.
Thurlow Cook
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
UMass, Umass Amherst, Math, Calculus, 127
KARMA
25 ?

## Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Monica Weisenbach on Saturday March 28, 2015. The Class Notes belongs to MATH127 at University of Massachusetts taught by Thurlow Cook in Spring2015. Since its upload, it has received 38 views. For similar materials see Calculus I for Life and Social Science Majors in Mathematics (M) at University of Massachusetts.

×

## Reviews for Week 7 of Lecture Notes

×

×

### 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: 03/28/15
Week 7 Lecture Notes Minimums and Maximums Remember minimums are low points maximums are high points Local minsmaxes relative minsmaxes Global minsmaxes absolute minsmaxes The roots of the first derivative give the critical points of the graph where the graph has minimums or maximums A sign change of positive to zero to negative is a maximum A sign change of negative to zero to positive is a minimum The roots of the second derivative give the inflection points of the graph where the graph changes concavity Example 1 fx 3x44x36 f x 12x312x2 gt 12x2x1 roots are 01 f x 36x224x gt 12x3x2 roots are 0 23 x 0 23 1 fX 6 54 5 f x o 17 o f X O 0 12 Charts like this are helpful by tracking the signs of the first and second derivatives Do this by testing numbers between the interval From this we can see that The concavity changes twice at O and 23 There is a minimum at 1 because the sign changes from to O to The critical point at 0 turns out to be nothing Try using this to draw the graph Example 2 fx X36X24X2 f x x22x21 roots are 21 f x x12 roots are 12 x 2 12 1 fx 36 25 5 f x O O625 O f x 15 O 12 From this we see that There is a maximum at 2 and a minimum at 1 There is an inflection point at 12 Try to draw the graph Example 3 fx x33x29x15 domain 54 watch the domain f x 3X26X9 gt 3X2 2X3 gt 3X3X1 roots are 1 3 f x 6x6 gt 6x1 roots are 1 x 5 1 1 3 fx 140 20 4 12 f x O o W o With the domain don t forget to Check the endpoints With this we see There is a maximum at 1 and a minimum at 3 There is an inflection point at 1 Try drawing the graph Graphs for the above check your work Example 1 Example 2 Example 3 Revenue Functions Revenue Rq is expressed as a function of quantity Rq pq revenue prioequantity Cost of producing the quantities Cq is also expressed as a function of quantity This has a fixed cost investment cost Profit revenue cost of producing items aka P RqCq Marginal revenue is the derivative of the revenue function R Marginal cost is the derivative of the cost function 0 How does one maximise profit Profit is maximised when marginal P canQ l In l39 a 25 I F RG Cql Pra f d39 1 011 a If a1 gt R q loss revenue R marginal cost 0 aka when the rate of money coming in the rate of money going out Example An ice cream company can sell 4000 units at 4 With a 025 decrease the number of units sold increases by 200 units Find the price and quantity that maximize revenue Rq pq 44000 16000 APAq O252OO 1800 locally the graph can be treated as a linear line In y mxb form p 1800qb p 18004000b b9 So p 1800q9 gt put this in the revenue function Rq pq 1800q9q q28009q R q 2q8009 q4009 set to zero Set to zero and q3600 Go back to p 1800q9 and p 180036009 45 So the answer is 3600 units at 450 Logistic Curve Growth Functions The equation is L1Cekt LC and k gt O and are constants L is the horizontal asymptote the upper limit L2 is the inflection point of the curve k affects the steepness of the curve and is the growth rate L P L1Cekt gt P1CektL gt PkCe39 kt Ce39ktP 0 L P kCektP1Cekt amp r if 1quot quotquotquot

×

×

×

### 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

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Allison Fischer University of Alabama

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over \$600 per month. I 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."

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

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.