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# Using Derivatives Chapter Exam

Exam Instructions:

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### Page 1

#### Question 1 1. Which of the following BEST describes point C?

#### Question 2 2. Where is the global minimum for the function f(x) = sin((pi)x) below between x=0 and x=2?

#### Question 3 3. Consider a balloon that you are inflating. It is a perfect sphere. If you are inflating it at a rate of F liters per minute (dV/dt = F), what is the equation for the change in radius as a function of time?

#### Question 4 4. Where is the global maximum for the function y=f(x) below between x=0 and x=2?

#### Question 5 5. What is the global minimum for the function f(x) = sin((pi)x) between x = 0 and x = 2?

### Page 2

#### Question 6 6. Which of the following is a local minimum?

#### Question 7 7. What is the formula for your bank balance given the following conditions:

#### Question 8 8. If h equals 3 m, and x is moving at a rate of 3 m / second, how fast is L changing when x equals 4m?

#### Question 9 9. What is the global minimum for the function y=f(x) below between x=0 and x=2?

#### Question 10 10. Solve the following differential equation for c=f(a).

### Page 3

#### Question 11 11. Which of the following BEST describes point B?

#### Question 12 12. What is the equation for L as a function of x?

#### Question 13 13. What is value of y at the finite local maximum for the function f(x) = 2x^3 - 3x^2?

#### Question 14 14. Given a population growth of 3%, how long will it take for the population to grow from 100 to 150?

#### Question 15 15. What is the value of x at the finite local minimum for the function f(x) = 2x^3 - 3x^2?

### Page 4

#### Question 16 16. You have a tank that is shaped like a prism that is on its side. The triangular base of the tank is a right triangle of height 10 m and width 10 m. See the image below. If the tank is being filled at a rate of 30 cubic meters per minute, how quickly is the height changing?

#### Question 17 17. Solve the following differential equation for y=f(x).

#### Question 18 18. The red car is traveling at 45 mph and the blue car is traveling toward the red car but is braking so that v(t) = 60 - 30t. In how many hours will they pass each other, assuming that they are 10 miles apart at t = 0?

#### Question 19 19. Which of the following BEST describes point A?

#### Question 20 20. Consider a balloon that you are inflating with a constant flow rate such that dV/dt is constant. It is a perfect sphere. How does dr/dt change as time moves forward?

### Page 5

#### Question 21 21. Solve the following differential equation for y=f(x) (assume that y is always positive).

#### Question 22 22. If the population of a city grows 25% in 3 years, what is the yearly growth rate?

#### Question 23 23. What is the global minimum for the function y=f(x) below between x=0 and x=2?

#### Question 24 24. What is value of y at the finite local maximum for the function y=f(x) below?

#### Question 25 25. Imagine you have a sheet cake with a width of 12 inches and a length of 12 inches. If you are smearing icing on it at a rate of 12 oz / minute, how quickly is the height of icing changing? One ounce is about 1 cubic inch of icing.

### Page 6

#### Question 26 26. Where is the global maximum for the function f(x) = sin((pi)x) between x=0 and x=2?

#### Question 27 27. Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cubic cm/min. How fast is the surface area of the balloon increasing when its radius is 16cm?

#### Question 28 28. The following differential equation represents the change in population as a function of time. What does the 0.03 represent in this equation?

#### Question 29 29. What is the equation of how L changes as a function of how x changes if h=6?

#### Question 30 30. The red and blue cars are 10 miles apart, but headed toward one another. The red car is traveling at 45 mph, and the blue car is traveling at a speed v(t). What is the equation for how the distance between them changes as a function of time?

#### Using Derivatives Chapter Exam Instructions

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