# Differential Calculus & Functions Chapter Exam

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### Page 1

#### Question 1 1. Decompose this composite function.

#### Question 2 2. Decompose this composite function in multiple ways.

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Question 3
3.
According to the mean value theorem, at how many points will the instantaneous rate of change equal the average rate of change between *x* = 1 and *x* = 3 on the following graph?

#### Question 4 4. What is the approximate instantaneous rate of change at point C?

#### Question 5 5. Find the derivative df/dt, given the function f(t).

### Page 2

#### Question 6 6. Find f'(x) for the following function.

#### Question 7 7. Find y'.

#### Question 8 8. Find y'(x).

#### Question 9 9. Does L'Hopital's rule apply to this problem? Why or why not?

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Question 10
10.
According to L'Hopital's rule, which of the following statements MUST be true for the equation shown below to hold?

A) f(x) and g(x) approach 0 or infinity

B) f'(C) does not equal 0

C) g'(x) does not equal 0

### Page 3

#### Question 11 11. Evaluate the derivative

#### Question 12 12. Find the derivative of f(x).

#### Question 13 13. Which of the following is the graph of a linear function?

#### Question 14 14. In the pictured graph of f(x) = x^2 + 6x, for which values of x is the function increasing?

#### Question 15 15. This graph represents a(n) _____ function.

### Page 4

#### Question 16 16. On the graph of a(n) _____ function, the left half of the graph exactly reflects the line or shape on the right half of the graph, except it is upside-down.

#### Question 17 17. What is the end behavior of a logarithmic function as x gets very large?

#### Question 18 18. What is the end behavior of an exponential function as x gets very large?

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Question 19
19.
If *f*(*x*) = *x* - 7 and *g*(*x*) = 2*x* + 9, find (*f* + *g*)(*x*).

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Question 20
20.
Suppose a company's revenue is modeled by the function *R*(*x*) = -0.1*x*2 + 3.7*x*, and the company's cost is modeled by the function *C*(*x*) = 0.008*x*3 - 0.1*x*2 + 1.8*x* - 10. Find the company's profit function *P*(*x*) = *R*(*x*) - *C*(*x*).

### Page 5

#### Question 21 21. What is the global minimum for the function f(x) = sin((pi)x) between x = 0 and x = 2?

#### Question 22 22. Where is the global minimum for the function f(x) = sin((pi)x) below between x=0 and x=2?

#### Question 23 23. According to Rolle's theorem, for a continuous function f(x), if the start point f(a) and the end point f(b) equal 0 then:

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Question 24
24.
If the continuous function g(t) equals 5 at the points t=2 and t=4, then what can you say about g(t)?

A) Between t=2 and t=4 there will be at least one point where the instantaneous rate of change is 0.

B) Between t=2 and t=4 the average rate of change is 0.

C) Between t=2 and t=4, g(t) is constant.

#### Question 25 25. How many discontinuities are in the function f(x) = (1 - x)/[(3 - x)(2 - x)]?

### Page 6

####
Question 26
26.
Which of the following functions are continuous?

I) f(x) = 1/(x-1),

II) f(x) = abs(x)-x,

III) f(x) = x^2/2

#### Question 27 27. Use the given formula to solve for z

#### Question 28 28. Using the given data, solve for z.

#### Question 29 29. How do you determine whether a function is an inverse of another function?

#### Question 30 30. Which of the following statements is true?

#### Differential Calculus & Functions 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!