business calculus ch2 practice test 1) is this the graph...

Business Calculus Ch2 Practice TestSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

1) Is this the graph of a function having the following properties?(I) concave down for all x(II) asymptotic to the line x = 0Enter your answer as just the word "yes" or the word "no" (lower case)

1)

2) Is this the graph of a function having the following properties?(I) defined for x -1(II) horizontal asymptote at y = 3(III) increasing for all x -1Enter just the word "yes" or the word "no" (lower case).

2)

3) Is this the graph of a function having the following properties?(I) x-intercept at x = -2(II) absolute maximum at x = -1(III) relative maximum at x = 1(IV) concave up for x 2Enter just the word "yes" or the word "no" (lower case).

3)

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4) Is this the graph of the function having the following properties?(I) inflection point at x = 3(II) no relative maximum point(III) asymptote at x = 5Enter just the word "yes" or the word "no" (lower case).

4)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

5) At which labeled point(s) is the function increasing? 5)

A) A, E B) A C) C, F D) E

6) At which labeled point(s) is the function decreasing? 6)

A) F B) C C) C, F D) A, E

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7) At which labeled point(s) is the graph concave up? 7)

A) C, D B) C, E C) C, D, E D) D

8) At which labeled point(s) is the graph concave down? 8)

A) B B) A, F C) A, B, F D) A, B

9) Which labeled point has the most positive slope? 9)

A) E B) F C) A D) B

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10) Which labeled point has the most negative slope? 10)

A) E B) D C) F D) C

11) Let F(x) be the function graphed below. For what value is F'(x) > 0? 11)

A) x < 0 and x > pB) p < x < qC) x > pD) 0 < x < qE) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

12) Points A, B, and C lie on the graph of a function f(x), as shown on the diagram. What arethe signs of f(x), f'(x), and f''(x) at the point C? Enter your answer as just "neg", "pos", or 0in the order given above separated by commas.

12)

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Choose the graph of a function having the given properties.13) Relative minimum points at x = 5 and x = 25; relative maximum point at x = 15; inflection points at

x = 10 and x = 20.13)

A)

5 10 15 20 25

B)

5 10 15 20 25C)

5 10 15 20 25

D)

5 10 15 20 25

14) From x = 0 to x = 10 the function increases and the slope decreases. When x > 10 the functiondecreases and the slope decreases (note: the slope is negative and becomes more negative).

14)

A)

10

5

B)

10

C)

10

D)

10

Solve the problem.15) The population of squirrels in a certain forest is increasing. Let P(t) be the population of squirrels at

time t and suppose that P(t) has the line y = 300,000 as an asymptote. What does this imply aboutthe size of the population?

15)

A) The population will grow to 300,000 then begin to drop.B) The population will not drop below 300,000.C) The population will not rise above 300,000.D) The population is 300,000 at any given time t.

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16) The graph below shows the price of a bushel of a certain crop over a span of 9 years. In what yearwas the rate of price increase the least?

9.27

1.27

1 2 3 4 5 6 7 8 9

16)

A) 6 B) 8 C) 2 D) 3

17) Which of the following could represent a function having the given properties?(I) increasing slope for x < 4(II) f'(x) > 0 for all x (x 4)(III) asymptote at x = 4

17)

A) B)

C) D)

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18) Is this the graph of a function having the following properties ?(I) f(0) = -5(II) f'(0) = 0(III) f''(0) = 12(IV) f( 7) = f(- 7) = -12Enter your answer as just "yes" or "no" (lower case).

18)

19) Is this the graph of a function having the following properties?(I) f'(x) > 0 for all x(II) f''(x) > 0 for all x < 0, f''(x) < 0 for x >0

(III) asymptotes at y =2

, y = -2

Enter your answer as just "yes" or "no" (lower case).

19)

20) Is this the graph of a function having the following properties?(I) f'(x) < 0 for all x(II) f''(x) > 0 for all x < 0(III) (0, 1) is a point on the graphEnter your answer as just "yes" or "no" (lower case).

20)

8


Solve the problem.21) Using the following properties of a twice-differentiable function y = f(x), select a possible graph of

f.

x y Derivativesx < 2 y > 0, y < 0-2 11 y = 0, y < 0-2 < x < 0 y < 0, y < 00 -5 y < 0, y = 00 < x < 2 y < 0, y > 02 -21 y = 0, y > 0x > 2 y > 0, y > 0

21)

A) B)

C) D)

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Suppose that the function with the given graph is not f(x), but f (x). Find the open intervals where the function is concaveupward or concave downward, and find the location of any inflection points.

22) 22)

A) Concave upward on ( , -1) and (0, 1); concave downward on (-1, 0) and (1, ; ); inflectionpointsat -1, 0, and 1

B) Concave upward on (-1, 0) and (1, ); concave downward on ( , -1) and (0, 1); inflectionpointsat -1, 0, and 1

C) Concave upward on (-1, 0) and (1, ); concave downward on ( , -1) and (0, 1); inflectionpointsat -2, 0, and 2

D) Concave upward on ( , 0); concave downward on (0, ); inflection point at 0

Suppose that the function with the given graph is not f(x), but f (x). Find the locations of all extrema, and tell whethereach extremum is a relative maximum or minimum.

23) 23)

A) Relative maximum at 1; relative minimum at -1B) Relative minimum at 0C) No relative extremaD) Relative maximum at 3; relative minimum at -3

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Solve the problem.24) The following graph represents f (x). At x = 70, does the graph of f(x) have a relative minimum, a

relative maximum, an inflection point, or none of these?

25 50 75 100

24)

A) none of these B) relative maximumC) relative minimum D) inflection point

25) Where is the function f(x) = 5(2x - 4)3

increasing? 25)

A) for x > 2 B) at x = 30 C) for all x D) none of these

Solve the problem.26) The following graph shows f (x). On what interval is f(x) decreasing?

2 6 10 14

26)

A) 8 < x < 14 B) 4 < x < 12 C) 0 < x < 8 D) 0 < x < 4

27) T(t) is the temperature on a cold day at time t hours. If T (8) = -4, by approximately how much willthe temperature drop from 8:00 to 8:15?

27)

A) 4 degrees B) 0.25 degrees C) 1 degrees D) 2 degrees

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28) Find the x coordinates of all relative extreme points of f(x) = 23

x3 - 7x2 + 24x - 72 28)

A) x = 0, 3, 4B) x = 3, 4C) x = -4, -3D) x = -4, -3, 0E) x = 2, 6

29) Find the x coordinates of all relative extreme points of f(x) = 12

x4 -23

x3 - 6x2 - 100 29)

A) x = -2, 0, 3 B) x = -3, 0, 2 C) x = 0 D) x = -3, 2 E) x = -2, 3

Find the relative extrema of the function, if they exist.30) s(x) = -x2 - 4x + 60 30)

A) Relative maximum at (-4, 60) B) Relative maximum at (-2, 64)C) Relative maximum at (2, 64) D) Relative minimum at (4, 60)

31) f(x) = x3 - 12x - 1 31)A) Relative maximum at (5, 64); relative minimum at (-3, 8)B) Relative maximum at (-2, 15); relative minimum at (2, -17)C) Relative maximum at (5, 64); relative minimum at (2, -17)D) Relative minimum at (-2, 15); relative maximum at (2, -17)

Find the points of inflection.32) f(x) = 7x3 + 2x + 7 32)

A) (0, 7) B) (2, 0) C) (0, 2) D) (7, 0)

33) f(x) = 2x3 + 3x2 - 12x 33)

A) -12

, 132

B) 0, 0

C) -2,32 D) No points of inflection exist

34) Find the inflection point(s) of f(x) = x33

-52

x2 + 6x - 36. 34)

A) 25

, f 25

B) 52

, f 52

C) x = -2, -3D) (10, f (10))E) (2, f(2)) and (3, f(3))

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35) If the second derivative of a function is f ''(x) = (x - 2)2(x2 - 9) is (2, f(2)) aninflection point?Enter just the word "yes" or "no" (lower case).

35)


36) Find the interval(s) where f is concave down for f(x) = -4x4 + 3x3 - 5x + 10. 36)

A) ( , 0) 38

,

B) 0, 38

C) ( , 0) (3, )D) ( , 0)

E) , 38

37) Which of the following is (are) true of f(x) = 5 + 3x2 - x3?(I) (1, 7) is a point of inflection(II) f(2) is a relative maximum point(III) f has a relative minimum point at x = 0(IV) f is increasing on (2, )

37)

A) II and IIIB) I, II, and IIIC) II, III, and IVD) all of theseE) none of these

38) Which of the following is (are) true of f(x) = 3x2/3 - 2x?(I) f is decreasing on (1, )(II) (1, f(1)) is a relative minimum point(III) f is concave down everywhere(IV) (0, 0) is an inflection point

38)

A) I and IIIB) II, III, and IVC) I, II, and IIID) all of theseE) I, III, and IV

13

Graph the function by first finding the relative extrema.39) f(x) = x3 + 3x2 - x - 3 39)

A) B)

C) D)

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40) g(x) = 3x4 - 8x3 40)

A) B)

C) D)

Sketch the graph and show all extrema, inflection points, and asymptotes where applicable.

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41) f(x) = 2x3 + 12x2 + 18x 41)

A) No extremaInflection point: (0, 0)

B) Rel max: (0, 0), Rel min: (-7, 343)Inflection point: (-3.5, 171.5)

C) Rel min: (2, 10)No inflection points

D) Rel max (-3, 0), Rel min: (-1, -8)Inflection point: - 2, - 4

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42) Is this the graph of f(x) = (x - 2)3 + 1?Enter just the word "yes" or "no" (lower case).

42)

43) Is this the graph of f(x) = 14

x4 - x3 + 2?

Enter just the word "yes" or "no" (lower case).

43)


Graph the function.44) f(x) = -x4 - 2x2 44)

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A) B)

C) D)

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45) f(x) = -2x(x - 1)2 45)

A) B)

C) D)

46) What is the maximum area that can be enclosed in a rectangular shape with 100 feet of fence if oneof the two long sides is not fenced (there is a natural boundary there)?

46)

A) 1250 square feetB) 625 square feetC) 2500 square feetD) 1000 square feetE) none of these

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47) Suppose that 20,000 fans will go to a ball game when the price of a ticket is $5.00, and that 500fewer fans will go for each $1.00 increase in ticket price. By how much should ticket prices beincreased (or decreased) in order to maximize revenue?

47)

A) increase price by $45.00 B) decrease price by $1.00C) increase price by $17.50 D) increase price by $22.50

48) A health club offers memberships at the rate of $300, provided that at least 50 people join. For eachmember in excess of 50, the membership fee will be reduced by $2 for all members. Due to spacelimitations, at most 125 memberships will be sold. How many memberships should the club sell inorder to maximize its revenue?

48)

A) 125B) 100C) 50D) 75E) none of these

Solve the problem.49) Find the price p per unit that produces the maximum profit P if C(x) = 30 + 80x and p = 84 - 2x. 49)

A) $8 B) $82 C) $78 D) $4

50) The annual revenue and cost functions for a manufacturer of precision gauges are approximatelyR(x) = 500x - 0.02x2 and C(x) = 120x + 100,000, where x denotes the number of gauges made. Whatis the maximum annual profit?

50)

A) $2,005,000 B) $1,905,000 C) $1,805,000 D) $1,705,000

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Answer KeyTestname: CH2PRAC

1) yes

2) yes

3) yes

4) yes

5) A6) C7) D8) C9) A

10) C11) C12) pos, 0, neg13) C14) B15) C16) A17) C18) no

19) yes20) yes

21) B22) B23) B24) B25) D26) B27) C28) B29) A30) B31) B32) A33) A34) B35) no36) A37) B38) A39) D40) B41) D42) yes

43) yes21

Answer KeyTestname: CH2PRAC

44) A45) D46) A47) C48) B49) B50) D

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business calculus ch2 practice test 1) is this the graph...

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