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Applications of Derivatives Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

Page 1

Question 1 1.

You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the equation for the volume as a function of only the cylinder radius?

Question 2 2. Evaluate f(1.1) by linearizing f(x) around x=1.

Question 3 3. You are standing on a building on Jupiter with a ball, and you have decided that the appropriate equation of motion for the height of the ball in miles as a function of (t) is shown below on the graph. What is the highest that the ball gets?

Question 4 4. How many times do you have to repeat Newton's Method to find an answer?

Question 5 5. You would like to use Newton's method to find the root of f(x). What is the equation you will need to solve?

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Question 6 6. You are designing a fence that surrounds a rectangular area where the length is 3 times as long as the width. The maximum amount of fencing you can use is 250 meters. What is the equation to figure out the length and width of your fence?

Question 7 7. Linearize f(x) about the point x:

Question 8 8. Evaluate f(2.1) by linearizing f(x) around x = 2.

Question 9 9. Evaluate f(pi + 0.1) by linearizing f(x) around x=pi.

Question 10 10. Evaluate f(2.2) by linearizing f(x) around x=2.

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Question 11 11. Where are the possible maximums and minimums located for this function?

Question 12 12.

You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the maximum volume you can obtain in a cylinder that costs $4?

Question 13 13. Our initial guess of 0 produced a y of -1 and a y' of 2. What is the next guess according to Newton's Method?

Question 14 14. Linearize f(x) about the point x=0:

Question 15 15. You have 100 ft of fencing to use to enclose part of a yard. You first choose to enclose the yard with a rectangular pen 'w' feet in width and 'd' feet in depth. As a function of 'w', what is the equation for the area that you can enclose using 100 ft of fence?

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Question 16 16. You have 150 ft of fencing to use to enclose part of a yard. You choose to enclose the yard with a rectangular pen 'w' feet in width and 'd' feet in depth. As a function of 'w' and 'd', what is the equation for the perimeter of the rectangle?

Question 17 17. Linearize f(x) about the point x=0:

Question 18 18. You are standing on a building 50m tall with a ball. You throw it up into the air at a velocity of 5 meters per second. It is accelerating downward at -9.8 meters per second squared. Which of the following equations describes the height of the ball as a function of time, t?

Question 19 19. Which of the following is true about Newton's Method?

Question 20 20. Evaluate f(1.1) by linearizing f(x) around x=1.

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Question 21 21. What is the maximum area that you can enclose in a rectangular pen with 150 feet of fencing?

Question 22 22. What is height as a function of distance along the earth?

Question 23 23. You can enclose a rectangular yard with a fence. The length of the longest side of the fence is going to be 2 times the length of the shortest side of the fence. Write the equation for the perimeter of the fence.

Question 24 24.

You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What are the equations for the surface area and volume of this cylinder?

Question 25 25. How do you find maximums and minimums of problems?

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Question 26 26. Sue has baked an apple pie and sliced it into 16 pieces. Every minute, one of Sue's friends takes a piece. After 7 minutes, how many slices are left?

Question 27 27.

Given the following problem, which of the following is crucial for you to solve it?

Mary has 4 sheep and 10 goats. John has 10 cats and 12 goats. Mark has 4 dogs, 3 cats, and 1 goat. How many goats do John and Mark have together?

Question 28 28.

You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the derivative of the equation for volume with respect to the cylinder radius?

Question 29 29. Linearize this function.

Question 30 30. A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river. He doesn't need fencing along the river. What are the dimensions of the field that has the largest area?

Applications of Derivatives Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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