### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Math 127 Study Guide for Exam 1 MATH127

UMass

GPA 3.819

### View Full Document

## About this Document

## 228

## 0

## Popular in Calculus I for Life and Social Science Majors

## Popular in Mathematics (M)

This 5 page Study Guide was uploaded by Monica Weisenbach on Saturday February 21, 2015. The Study Guide belongs to MATH127 at University of Massachusetts taught by Thurlow Cook in Spring2015. Since its upload, it has received 228 views. For similar materials see Calculus I for Life and Social Science Majors in Mathematics (M) at University of Massachusetts.

## Popular in Mathematics (M)

## Reviews for Math 127 Study Guide for Exam 1

### 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: 02/21/15

Study Guide for Math 127 Important Algebra to Remember A function is a relation between the domain x input and the range y output There is only one x per y but can be multiple X s per y Vertical Line Rule a vertical line drawn through the graph should only hit the graph once Slope is the average rate of change found with the equation Y1YoX1Xo slope gt 0 means the graph is increasing slope lt 0 means the graph is decreasing the slope of a horizontal line is O a vertical line has no slope and is not a function A linear function is represented by the equation ymxb m is the slope riserun and b is the yintercept A quadratic equation is yx2 possibly combined with a linear equation yax2bxc with c being the yintercept Quadratics can be solved to find the roots X s by factoring or the quadratic equation bb24ac2a Sinx and cosx are periodic functions They both have a period of 211 as both functions are derived from circles and both have an amplitude of 1 so the range is 1gtgt1 For AsinBx A is the amplitude and the period of B2n Logabx means aXb just plain og without an added base is base 10 and In is base e e standing for Euler s number No logarithms of negative numbers Manipulating Functions and Graphs fx2x1 gxx21 New functions can be created from operations with these ones fgx fXgX 2X1 X21 X22X2 fgx fXgx 2X1 X21 2X1X21 X22X fgx fXgX 2X1X21 2X32XX21 2X3X22X1 fgX fX21 2X2 2X221 2X23 gfX g2X1 2X121 4X24X1 1 4X24X2 fgx fxgx 2X1x21 gfx gxfx x212x1 Graphs can be easily manipulated as well take yx2 Try it on a calculator x22 will move the graph to the right two units x22 will move the graph to the left two units x22 will move the graph up two units x22 will move the graph down two units 2X2 will shrink the graph 5x2 will expand the graph Continuity To be continuous at a point the graph must be unbroken For example X2 is continuous at all points while X22x2 has a hole at x2 because that value of x makes a dividebyzero error E Con rm ouS N 0139 Carthnu ouS What is a Derivative The derivative is the instantaneous rate of change It s the slope of a point and another point very close to it So close it s basically O The other point is on a line tangent to the point on the equation means it s linear Some notations for derivative is f x AyAx dxdy ddy It s important to note that the derivative is not the same for each point The formula for the derivative is lim hgtgtO fxhfxh The equation derived from this formula works to find the derivative for all points The derivative of a linear function is m for all points A constant has a derivative of zero If f x is positive the graph is increasing and if f x is negative the graph is decreasing At the very top of a curve the derivative is a horizontal line and therefore 0 As the distance h between xa and the other points decreases the line gets steeper and steeper until it becomes the tangentHne Ex What s the derivative of fxx2 lim xh2x2 x22xhh2x2 2xhh2 h2xh 2Xh 2xO 2x hgtgtO h h h h 1 1 Remember to take the limit after the h is canceled out of the bottom Power Functions Power functions x to a constant power follow a rule with their derivatives The rule for power function derivatives is as follows f x of XN NXN1 ExponenHaIFunc ons Exponential functions a constant to a variable power also have a rule with their denva ves The rule for the derivative of exponential functions is f x of NX NXlnN For the function fxeX the derivative would be simply eX as In is base e Manipulating Derivatives 39 fg X f X J X af x af x Using the above rules and the rules for power or exponential functions can make finding derivatives of more complex functions easier If you have an equation like y4x33x25x22 you can take the derivative from each term 4x343x2 3x232x 5x5 220 leading to 12x26x5 Second Derivatives The second derivative comes from taking the derivative of a function s derivative The second derivative is written as f x f f x gt O the graph is concave up If f x lt O the graph is concave down

### 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

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

#### "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!"

#### "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."

### 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.