Final Review

1
Final Review

• Calculus I, Fall 2006

2

• Given a percent growth rate of 10, what is the
  value of a in the equation f(x)Pax

• 0.01
• 0.001
• 1.10
• 1.01
• None of the Above

3

• Find the indefinite integral of the function
  graphed below

• lnsec(s)tan(x)C
• sec2(x)C
• lnsec(x)C
• tan(x)C
• None of the Above

4

• Given logbxA, what is the equivalent exponential
  expression?

• xAb
• lnAx
• bAx
• bAx
• None of the Above

5

• Given the graph of f(x)x(x2-3) below, what is
  the area between the curve and the x-axis from 0
  to 1?

• 1/4 - 3/2
• 3/2 1/4
• -2
• 2
• None of the Above

6

• Exponential functions have a constant rate of
  change

• TRUE
• FALSE

7

• What is the equation describing the following
  graph?

5
3
1
2?
4?
6?
-2?
-4?
-6?
8

• Given the graph of f(x)x(x2-3) below, what is
  the total change in the anti-derivative function
  F(t) from -1 to 1?

9

• Given y16sin(2x)5, what is the period?

• 2?
• 4?
• 2
• ?
• None of the Above

10

• What is the equation describing the following
  graph?

1
-?
-?/2
-3?/2
?/2
?
3?/2
-1
11

• logb(CD)logbClogbD

• TRUE
• FALSE

12

• Which of the following is the graph of

B
A
D
C
E None of these
13

• Given the following graph of g(x), order
• a) g(2)
• b) average value of g(x) over the interval 0
• c) Integral of g(x) from 1 to 3
• from least to greatest.

• a
• a
• c
• c
• None of the Above

14

• Given F(x)f(x), what does the shaded region
  represent?

F(x)
15

• Given the graph of f(x), which of the following
  is the graph of f(xk)?

A
B
C
D None of these
16

• The following graph shows the velocity of a
  rocket taking off from earth versus time. When
  did the rocket hit the ground?

2
4
6
8

• t2
• t4
• t6
• t8
• None of the Above

17

• Given the following graph of g(x), determine
  which of the following statements are true about
  the anti- derivative.

g(x)
2
4
6
8

• G(t) is positive for all 0
• Over the interval 1
• G(t) is concave up at t 1/2

• i only
• ii only
• iii only
• i and ii only
• ii and iii only
• None of the above

18

• Given sin2(?)-1x, x is equal to

19

• Given the following table of values, find a
  formula for f (x)

20

• Evaluate the following integral

21

• A person runs around a circular track. Their
  horizontal distance from the starting line is a
  periodic function. If the track is 400 meters
  long, and the runner takes 1 minute to run
  completely around the track once, which of the
  following equations could model the distance from
  the starting line as a function of time given the
  runner starts running at time t0?

22

• Evaluate the following integral

23

• The total number of undergraduate students at the
  Willamette University is given in the following
  table. What was the average rate of change in
  the number of students from 1990 to 2005?

24

• Given a runners horizontal distance from the
  starting line on a circular track is given by the
  equation
• d 200sin(2?x)
• Which of the following formulas gives the
  total horizontal distance run in 4 minutes?

25

26

• Find the critical points of

27

28

29

30

• Given F(x)f(x), the shaded area on the graph of
  f(x) represents

1
b
a
-1
31

• What is the derivative of

32

• Given F(x)f(x), the marked quantity on the
  graph of f(x) represents

a
b
A14
33

• Given F(x)f(x), which of the following
  represents
• on the graph of F(x)?

1
B
A
-?
-?/2
-3?/2
?/2
-?
-?/2
-3?/2
?/2
a
a
b
a
b
?
3?/2
a
b
-1
-1
C
D. None of the above
-?
-3?/2
?/2
a
b
-1
34

• Given F(x)f(x), which of the following
  represents f(a) on the graph of F(x)

1
A
B
a
a
-?
-?/2
-3?/2
?/2
?
3?/2
-1
D. None of the above
C
a
35

36

37

38

39

40

41

42

43

44

45

46

47

• What is the amplitude of the function

48

• Fill in the blanks

• Concave down b. decreasing
• c. zero d. inflection point
• Concave up f. increasing
• g. Max of Min h. critical point

49

• Which is the best method to use to integrate

50

51

• is the derivative
  of

52

• Which of the following equations describes the
  graph of the sine function shifted down by C
  units, left by D units, stretched horizontally by
  A units, and vertically by B units?

53

54

• What is the equation describing the following
  graph?

5
2
4
6
-2
-4
-6
55

• Given f(t) gives the velocity of a ball in feet
  per second as a function of the time in seconds
  since the ball was thrown into the air, what are
  the units of

• seconds
• ft/sec
• feet
• ft/sec2
• None of the above

56

• Given F(5)6, use the graph of F(x) below to
  find F(-4).

A35
A14

• F(-4)-2
• F(-4)14
• F(-4)16
• None of the above

57

• Which of the following is a possible formula for
  the function graphed below?

58

• Given 3log(x)12, which of the following must be
  true?

• x1036
• 3x1012
• x31012
• x104
• None of the Above

59

• Given 19t525, what is t?

60

• Which of the following formulas is/are correct?

61

• Given f(x)axb, when a is greater than one,
  f(x) is everywhere ______________.

• positive
• negative
• increasing
• decreasing
• None of the Above

62

• Given the following graph of F(x), which are
  inflection points of F(x)?

• A, C, F, K, M
• E, G, M
• E, G
• B, D, H, I, J, L, N
• None of the Above

63

• Suppose p is a critical point of the function
  f(x). p is a local minimum if _____________.

• f(p) is positive
• f(p) is negative
• f(x) switches from positive to negative at p
• f(x) switches from negative to positive at p
• None of the Above

64

• Given Aln(x)C, what is x?

65

• Find the second derivative of f(x)-13x5

66

• Given the following graph of the derivative
  F(x), which are inflection points of F(x)?

• A, C, F, K, M
• E, G, M
• E, G
• B, D, H, I, J, L, N
• None of the Above

67

• Given the following graph of the derivative
  F(x), which are local minima or maxima of F(x)?

• A, C, F, K, M
• E, G, M
• E, G
• B, D, H, I, J, L, N
• None of the Above

68

• How many critical points does f(x)2x3 have?

• 0
• 1
• 2
• 3
• None of the Above

69

• What is the global maximum of f(x)-(x-2)24

• (-2,4)
• (4,-2)
• (4,2)
• (2,4)
• None of the Above

70

• Where is f(x)x3 concave up?

• (-?, ?)
• (- ?,0
• 0, ?)
• (0, ?)
• None of the Above

71

• Given F(x)f(x), the marked quantity on the
  graph of f(x) represents

a
b
A14
72

• The following is a graph of the velocity of two
  cars A and B. Given this graph, which of the
  following statements are true?

• Car A travels further
• Car A went faster
• Car A stops first
• Car B travels further
• Car B went faster
• A, B, and C
• B, C, and D
• A, C, and E
• None of these

73

• For which graph is the statement has a local
  and global minimum at x3, but no local or global
  maximum true?

A
C
B
D
E. None of these
74

• Which of the following is the graph of F(x),
  which is the graph of F(x), and which is the
  graph of F(x)?

75

• Between x-1 and x2, the graph of the derivative
  f(x) is __________.

• increasing
• decreasing
• both
• neither

f(x)
76

• Between x-1 and x2, the graph of the derivative
  f(x) is __________.

• positive
• negative
• both
• neither

f(x)
77

• Which of the following statements can be true of
  a continuous function F(x) for -? x ?

• 1
• 2
• 3
• 1 and 2
• 1, 2, and 3
• None of these

• F(x)0, F(x)0
• F(x)
• F(x)0, F(x)0