1. Find the absolute minimum and absolute maximum values of *f* on the given interval. *f*(*x*) = ((*x^2)* − 1)^3, [−1, 4]

absolute minimum( ) absolute maximum( )

2. Find the absolute maximum and absolute minimum values of *f* on the given interval.

*f*(*t*) = 2 cos(*t*) + sin(2*t*), [0, *π*/2]

absolute minimum( ) absolute maximum( )

3. Find the absolute minimum and absolute maximum values of *f* on the given interval.

*f*(*t*) = 3*t* + 3 cot(*t*/2), [*π*/4, 7*π*/4]

absolute minimum( ) absolute maximum( )

4. Find the absolute maximum and absolute minimum values of *f* on the given interval.

*f*(*t*) =t*sqrt (64-t^2) [−1, 8]

absolute minimum( ) absolute maximum( )

5. Find the absolute maximum and absolute minimum values of *f* on the given interval.

*f*(*x*) = *xe^(*−*x*2/72), [−5, 12]

absolute minimum( ) absolute maximum( )

6. Find the absolute minimum and absolute maximum values of *f* on the given interval.

*f*(*x*) = *x* − ln(2*x*) [1/2 , 2]

absolute minimum( ) absolute maximum( )

7. Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)

( )m (smaller value)

( ) m (larger value)

8. Find the dimensions of a rectangle with area 1,000 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)

( )m (smaller value)

( ) m (larger value)

9. A model used for the yield *Y* of an agricultural crop as a function of the nitrogen level *N* in the soil (measured in appropriate units) is

*Y* =KN/(9+N^2)

where *k* is a positive constant. What nitrogen level gives the best yield?

N=( )

10. The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function

*P* = 120i/(i^2 + i +4)

where *I* is the light intensity (measured in thousands of foot-candles). For what light intensity is *P* a maximum?

i= ( ) thousand foot-candles

11. Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

Finish solving the problem by finding the largest volume that such a box can have.

V=( )ft^3

12. A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used.

sides of base =( )m

height =( )m

13. If 1,200 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

( )cm^3

14. (a) Use Newton’s method with *x*1 = 1 to find the root of the equation

*x^3* − *x* = 4

correct to six decimal places.

*x* = ( )

(b) Solve the equation in part (a) using *x*1 = 0.6 as the initial approximation.

*x* = ( )

(c) Solve the equation in part (a) using *x*1 = 0.57. (You definitely need a programmable calculator for this part.)

*x* = ( )

15. Use Newton’s method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

3 cos *x* = *x* + 1

*x* = ( )

16. Use Newton’s method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

(*x* − 5)^2= ln(*x*)

x=( )

17. Use Newton’s method to find all real roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

8/x=1+x^3

x=( )

18. A particle is moving with the given data. Find the position of the particle.

*v*(*t*) = 1.5*sqrt(t) *s*(4) = 13

s(t)=( )

19. Find *f*.

*f* *”*(*θ*) = sin(*θ*) + cos(*θ*), *f*(0) = 2, *f* *‘*(0) = 3

*f*(*θ*) = ( )

20. Find *f*.

*f* *”*(*x*) = 4 + cos(*x*), *f*(0) = −1, *f*(7*π*/2) = 0

*f*(*x*) = ( )

21. Find *f*.

*f* *”*(*t*) = 3*e^t* + 8 sin(*t*), *f*(0) = 0, *f*(*π*) = 0

*f*(*t*) = ( )

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.