Prepare for your exams
Get points
Guidelines and tips

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study

Go to the blog

Past Test 4 Part A - Functions and Engineering Calculus I | MATH 129, Exams of Mathematics

Christian Brothers University (CBU)Mathematics

Prof. Cathy W. Carter

Material Type: Exam; Professor: Carter; Class: Functions/Engr Calculus I; Subject: Mathematics; University: Christian Brothers University; Term: Summer 2008;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-80k 🇺🇸

10 documents

1 / 5

This page cannot be seen from the preview

Don't miss anything!

Math 129 Test 4 – Part I Name___________________________

Show all work in order to receive credit. 11/7/08

Calculator-free. In each question, if any is implied.

4 3

( ) 4 10f x x x  

(15 pts)

a. Find the first and second derivative and construct charts for each.

b. Use the information in your charts to answer the following.

The function has critical points at __________.

The function increases on __________________ and decreases on _____________________.

The function has relative maximum(a) of __________ at __________.

The function has relative minimum(a) of __________ at __________ .

The function is concave up on _______________ and is concave down on ________________.

The function has inflection point(s) of ________________.

c. Find other key points if appropriate and sketch the graph.

d. What is the domain & range of the function?

e. Find the absolute maximum and absolute minimum on

0 2x 

or state that they don’t exist.

Partial preview of the text

Download Past Test 4 Part A - Functions and Engineering Calculus I | MATH 129 and more Exams Mathematics in PDF only on Docsity!

Math 129 Test 4 – Part I Name___________________________ Show all work in order to receive credit. 11/7/ Calculator-free. In each question, if any is implied.

f ( ) x  x^4  4 x^3  10 (15 pts) a. Find the first and second derivative and construct charts for each. b. Use the information in your charts to answer the following. The function has critical points at __________. The function increases on __________________ and decreases on _____________________. The function has relative maximum(a) of __________ at __________. The function has relative minimum(a) of __________ at __________. The function is concave up on _______________ and is concave down on ________________. The function has inflection point(s) of ________________. c. Find other key points if appropriate and sketch the graph. d. What is the domain & range of the function?

e. Find the absolute maximum and absolute minimum on 0  x  2 or state that they don’t exist.

Use l’Hopital’s rule to find the following limits: (10 pts) a. (^2)

lim

x   x

2 1

lim

x ln 2

x

 x

The radius of a spherical balloon is increasing at the rate of 2 inches per minute. Find the rate of change of the volume when the radius is 6 inches. (Recall 3

V sphere   r .) (8 pts)

4. The total deficit since 2002 of a small country can be modeled by the function ( ) 12 8 4

D t te



  in billions

of dollars. (12 pts) a. What is the rate of change of the total deficit in 2004? b. Is the total deficit increasing or decreasing in 2004? Clearly explain why. c. If the model remains true, will the total deficit be increasing or decreasing in 2010? Justify.

6. ( )^3

x g x x x

(10 pts)

a. What is the domain?

b. Find any asymptotes.

c. Find any x and y intercepts.

d. Find the first derivative and construct a chart for it.

e. Use the information in your charts to answer the following. The function has critical points at _____________. The function increases on __________________ and decreases on _________________. The function has relative maximum(a) of __________ at __________. The function has relative minimum(a) of __________ at __________. f. Find other key points if appropriate and sketch the graph.

Suppose that you are using Newton’s Method to estimate the solution of x^4 + x = 3. For your initial guess use xo = 1. Find x 1. (10 pts)

a. Find the local linearization of

1  x

near x = 3. b. Use your result in part (a) to estimate

. (10 pts)

Four feet of wire is to be used to form a square and a circle. Let x denote the length of the side of the square. a. How much of the wire should be used for the square so that the total area is maximized? b. How much of the wire should be used for the square so that the total area is minimized? (Allow for the possibility that all of the wire is used for the square or the circle.) (10 pts)