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Calculations & 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. Find the derivative of f(x).

Question 2 2. Find the second derivative of y(x).

Question 3 3. Evaluate.

Question 4 4. Evaluate the derivative.

Question 5 5. Find the derivative df/dk.

Page 2

Question 6 6. Find the derivative df/dt.

Question 7 7. Which of the following is true about this graph?

Question 8 8. The first derivative gives you which one of the following?

Question 9 9. Which is the symbol for the first derivative?

Question 10 10. What is the highest-order derivative of f(x) that is NOT zero?

Page 3

Question 11 11. Find the jerk of the function shown below:

Question 12 12. Evaluate the following second order derivative.

Question 13 13. Which of the following are true statements?

Question 14 14. What is true about the derivative of a function at a maximum or minimum point of the function?

Question 15 15. Suppose we found the point (3,19) to be a minimum point of the function f. What must be true about the second derivative of f evaluated at x = 3?

Page 4

Question 16 16. Find the derivative of f(x).

Question 17 17. Find the derivative of f(x).

Question 18 18. Find the derivative of f(t).

Question 19 19. Evaluate the following.

Question 20 20. Evaluate.

Page 5

Question 21 21. Differentiate f(x).

Question 22 22. Find the derivative of f(x).

Question 23 23. Find the derivative df/dx.

Question 24 24. Given the derivative of a function (ƒ′(x)), which of the following could be ƒ(x)?

Question 25 25. Which of the following BEST explains what an optimization problem asks you to do?

Page 6

Question 26 26. A rectangular area of 3,200 square feet is to be fenced off. Two sides of the fence will be using fence costing $1 per foot and the other two sides will be using fence costing $2 per foot. Find the lowest possible cost for the fence and the dimensions that give this cost.

Question 27 27. A cylindrical container must hold 2L or 2,000 cm^3 of liquid. Find the dimensions of the container which will minimize the amount of material needed.

Question 28 28. Find the derivative of p(t).

Question 29 29. Find the derivative of f(x).

Question 30 30. Which of these first derivatives shows a decreasing function?

Calculations & 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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