Review for Test 2 - Arizona State Universitychoi/MAT210/MAT210_test2_Review...____ 16. The Thoroughbred Bus Company finds that its monthly costs for one particular year were given

Name: ______________________ Class: _________________ Date: _________

1

Review for Test 2

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. For the cost function, find the marginal cost at the given production level x.

C(x) = 10,000 + 5x − x2

10,000, x=1,000

a. $4.80 per itemb. $5.00 per itemc. $4.81 per itemd. $5.20 per iteme. $4.78 per item

____ 2. Find the value of x for which the marginal profit is zero.

C(x) = 2x, R(x) = 7x − x2

2,000

a. x = 2,500b. x = 10,000c. x = –5,000d. x = 5,000e. x = 7,000

____ 3. The cost, in thousands of dollars, of airing x television commercials during a Super Bowl game is given by the formula

C(x) = 250 + 1,500x − 0.002x2 .

Estimate how fast (in dollars per television commercial) the cost is going up when x = 8.

a. $1,499,968b. $1,500,032c. $1,500d. $1,500e. $1,499,984

2

____ 4. The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula

C(x) = 250 + 30x − 0.005x2 .

Evaluate the average cost C(100).

a. $29.50b. $3,249.50c. $28.00d. $3,200.00e. $32.00

____ 5. Your monthly profit (in dollars) from selling magazines is given by P (x) = 4x + 3 x where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.

a. P(100) = $430, P'(100) = $4.15b. P(100) = $417.32, P'(100) = $0.35c. P(100) = $860, P'(100) = $4.65d. P(100) = $417.32, P'(100) = $4.15e. P(100) = $215, P'(100) = $2.08

____ 6. According to the equation given, a toy manufacturer calculates its daily profit P (in dollars) based on the number of workers n it employs.

P = 400n − 0.4n 2

Calculate the marginal product at an employment level of 100 workers.

a. $320b. $36,000c. $440d. $39,960e. $3,999,960

3

____ 7. Your company is planning to air a number of television commercials during the ABC television network's presentation of the Academy Awards. ABC is charging your company $795,000 per 30-second spot. Additional fixed costs (development and personnel costs) amount to $400,000, and the network has agreed to provide a discount of D(x) = 5,000 x for x television spots. Compute marginal cost C ' (3) and average cost C(3).

a. C ' (3) = $925,447 per spot; C(3) = $859,502 per spotb. C ' (3) = $925,447 per spot; C(3) = $793,557 per spotc. C ' (3) = $793,557 per spot; C(3) = $925,447 per spotd. C ' (3) = $792,557 per spot; C(3) = $925,447 per spote. C ' (3) = $793,557 per spot; C(3) = $925,347 per spot

____ 8. The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:

C(q) = 5,000 + 200q 2

where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?

a. $700b. $7,800c. $2,800d. $2,100e. $1,400

____ 9. Your Porsche's gas mileage (in miles per gallon) is given as a function M(x) of speed x in miles per hour. It is found that

M ' (x) =4,900x−2 − 1

(4,900−1 + x)2.

Find M '(30), M '(70) and M '(95).

a. M '(30) = 0.0001, M '(70) = –0.0049, M '(95) = 0b. M '(30) = 0.0001, M '(70) = 0, M '(95) = –0.0049c. M '(70) = 0.0049, M '(30) = 0, M '(95) = –0.000051d. M '(30) = 0.0049, M '(70) = 0, M '(95) = –0.000051e. M '(70) = 0.0049, M '(70) = 0, M '(95) = –0.000051

4

____ 10. Calculate dydx

. You need not expand your answer.

y = x3.6

+ 3.6x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ x 2 + 4Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. 2x 13.6

− 3.6

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃

b. 13.6

− 3.6

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ x 2 + 4Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ − 2x x

3.6+ 3.6

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

c. 13.6

− 3.6

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ x 2 + 4Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ + 2x x

3.6+ 3.6

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

d. 2x 13.6

− 3.6

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + x

3.6+ 3.6

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ x 2 + 4Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

e. 2x


.

y = x 2 (2x + 3 ) (5x + 5 )

a. 2x 3 + 75x 2 + 30x

b. 25x2 + (2x + 3) (5x + 5 )

c. 2x 2 + 75x + 30

d. 65x2 + (2x + 75) (5x + 5 )

e. 40x 3 + 75x 2 + 30x

5


.

y = x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃

a. 12 x

x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + 1

2 x+ 8

x 3

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

b. 12 x

x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + 1

2 x− 8x

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃

x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

c. x2

x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + x

2− 8

x 3

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

d. 12 x

x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + 1

2 x− 8

x 3

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

e. 1x

x + 4

x 2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃ + 1

x− 8

x

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃

x + 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜


. You need not expand your answer.

y = 2x − 3(x − 5)(x − 1)(x − 4)

a.2(x − 5)(x − 4) − (3x 2 − 20x + 29)

((x − 5)(x − 4)) 2

b.2(x − 5)(x − 1)(x − 4) − (3x 2 − 20x + 10)(2x − 3)

(x − 5)(x − 1)(x − 4)

c. 2

3x 2 − 20x + 10

d.2(x − 5)(x − 1)(x − 4) + (3x 2 − 20x + 10)(2x − 3)

((x − 5)(x − 1)(x − 4)) 2

e.2(x − 5)(x − 1)(x − 4) − (3x 2 − 20x + 29)(2x − 3)

((x − 5)(x − 1)(x − 4)) 2

6

____ 14. Compute the derivative.

ddx

(x 3 + 3x)(x 2 − x)È

Î

ÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇

||||

x = 2

a. 78b. 59c. 92d. 72e. 36

____ 15. Find the equation of the line tangent to the graph of the given function at the point with x = 0.

f(x) = x + 1x + 2

a. y = -0.5b. y = -0.25x + 0.5c. y = --0.25x + 0.5d. y = --0.25xe. y = 0.5

____ 16. The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by

C( t) = 50 + t2 dollars after t months. After t months, the company had P( t) = 500 + t2 passengers per month. How fast was its cost per passenger changing after 3 months?

a. -$0.18 per monthb. $0.29 per monthc. $0.01 per monthd. $0.10 per monthe. $0.39 per month

7

____ 17. The "Verhulst model" for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula:

R(p) = r1 + kp

where p is the total population in thousands of organisms, r and k are constants that depend on the particular circumstances and organism being studied, and R(p) is the reproduction rate in thousands of organisms per hour. If k = 0.05 and r = 40, find R '(p).

a. 2

(1 + 0.05p) 2

b. - 2

(1 + 0.05p) 2

c. 21 + 0.05p

d. 40

1 + 0.05p 2

e. 2

1 + 0.05p 2

____ 18. Find dydx

using implicit differentiation.

x2 − 18y = 8

a. x18

b. - 118

c. x9

d. -9e. 8

8

____ 19. Calculate the derivative of the function.

g (x)=(2x2 + 2x + 3) -3

a. g '(x) = ( -6x2 + 6x + 9 ) -4

b. g '(x) = -3 (4x + 2)(2x2 + 2x + 3)

c. g '(x) = -3(2x2 + 2x + 3 ) -4

d. g '(x) = -12 (2x2 + 2x + 3 ) -4

e. g '(x) = -3 (4x + 2 ) (2x2 + 2x + 3 ) -4

____ 20. Calculate the derivative of the function.

s(x) = 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

5

a. s ' (x) = 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4 47

(5x − 2) 2

b. s ' (x) = -5 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4 12

(5x − 2) 2

c. s ' (x) = -5 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4 47x

(5x − 2) 2

d. s ' (x) = 5 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4

e. s ' (x) = -5 6x + 75x − 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4 47

(5x − 2) 2

9

____ 21. Find the indicated derivative. The independent variable is a function of t.

y = x 0.5 (1 + x);dydt

= ?

a.dydt

= (0.5x -0.5 ) dxdt

b.dydt

= (1.5x0.5 ) dxdt

c.dydt

= (0.5x -0.5 + 1.5x0.5 ) dxdt

d.dydt

= (0.5x -0.5 + 2.5x 0.5 ) dxdt

e.dydt

= (0.5x 0.5 + 2.5x0.5 ) dxdt

____ 22. Find the indicated derivative.

y = 8x3 + 11x

, x = 5 when t = 1, dxdt

|||t =1

= 11;dydt

||||t =1

= ?

Please round the answer to the nearest hundredth.

a.dydt

||||t = 1

= 1315.16

b.dydt

||||t = 1

= 13151.60

c.dydt

||||t = 1

= 6595.16

d.dydt

||||t = 1

= 599.56

e.dydt

||||t = 1

= 2175.80

10

____ 23. Find the indicated derivative.

y = 6 x + 6x

, x = 10 when t = 1, dxdt

|||t = 1

= 15;dydt

||||t = 1

= ?

Please round the answer to the nearest hundredth.

a.dydt

||||t = 1

= 128.07

b.dydt

||||t = 1

= 18.73

c.dydt

||||t = 1

= 0.85

d.dydt

||||t = 1

= 25.61

e.dydt

||||t = 1

= 12.81

____ 24. Compute the indicated derivative using the chain rule.

y = 8x + 2; dxdy

a. 12

b. -4c. -2

d. 18

e. 8

11

____ 25. Compute the indicated derivative using the chain rule.

y = 10x 2 − 7x ; dxdy

||||x = 2

a. 710

b. 2

c. 133

d. 113

e. 107

____ 26. Find the derivative of the following function.

f(x) = log 7 4x

a. 7x ln(4)

b. 14x ln(7)

c. 4x ln(7)

d. 1x ln(7)

e. none of these

12

____ 27. Find the derivative of the function.

f(x) = (x 9 + 8) ln x

a.x 8 (1 + 9 ln x) + 8

x

b.x 9 (1 + ln x) + 8

x

c.x 9 (9 + 9 ln x) + 8

x

d.x 9 (1 + 9 ln x) + 8

xe. none of these


f(x) = ln(5x + 3) 6

(4x + 2) 9 (8x + 9)

|||||

|||||

a. 305x + 3

− 364x + 2

− 88x + 9

b. 305x + 3

+ 364x + 2

+ 88x + 9

c. 5

(5x + 3) 6− 4

(4x + 2) 9− 8

8x + 9

d. 5

(5x + 3) 6+ 4

(4x + 2) 9+ 8

8x + 9

e. none of these

13


r(x) = ln (x 7 )È

Î

ÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇

4

a.28[ln (x 6 )]3

x 7

b.28[ln (x 7 )]3

x 7

c.28[ln (x 7 )]3

x

d.28[ln (x 7 )]4

x 7

e. none of these


r(x) = ln 2x + e 2x|||

|||

a. 2 + 2e 2x

2x + 2e 2x

b. 2 + 2e 2x

2x + e 2x

c. 2 + e 2x

2x + 2e 2x

d. 2 + e 2x

2x + e 2x

e. none of these

14


f(x) = e 5x 7ln 4x

a. 35e5x 7x 7 ln 4x + 4e 5x7

x

b. 35e5x 7x 6 ln 4x + e 5x7

4

c. 7e5x 7x 6 ln 4x + 4e 5x7

x

d. 35e5x 7x 6 ln 4x + e 5x7

x

e. 35e5x 6x 6 ln 4x + e 5x7

x


h (x) = e5x 2 − 2x + 1

x

a. 10x 3 − 2x 2 − 1

x 2e

5x2 − 2x + 1x

b. 5x 3 − 4x 2 − 1

x 2e

5x2 − 2x + 1x

c. 5x 3 − 4x 2 − 1x

e5x2 − 2x + 1

x

d. 10x 2 − 2x − 1x

e5x2 − 2x + 1

x

e. none of these

15

____ 33. Find the equation of the straight line, tangent to y = e3x log 8 x at the point (1, 0).

a. y (x) = e 3

ln 8x − e 3

ln 8

b. y (x) = e 8

ln 3x − e 8

ln 3

c. y (x) = e 8

ln 3x + e 8

ln 3

d. y (x) = e 3

ln 8x + e 3

ln 8e. none of these

____ 34. Find dydx


exy = 9

a. yex

b. xe x

9

c. - 1y

d. -ye. 1 − y

____ 35. Find dydx


y lnx + y = 10

a. -y

x (ln x + 1)

b.y

x ln x

c.y

x (ln x + 1)

d. - 1x (ln x + 1)

e. - xy (ln y + 1)

16

____ 36. Find dydx


x2 + y2 = 6

a. 2y

b. -yx

c. - xy

d. 2x + 2ye. 2x

____ 37. Find dxdy


(xy )2 + y2 = 3

a. 2y + 2x

b. - xy

c. -(x 2 + 1)

xy

d.xy

(x 2 + 1)

e.xy

x2 + 1

17

____ 38. Find dydx


xey− yex = 10

a.y − 1x − 1

b.ye x − e

y

xey− e x

c.ye

y+ e x

xey− e x

d. xe x + ey

yey

+ e x

e. xey− e x

ye x − ey

____ 39. Find dsdt


est = s5

a. s 4

5s 4 − te st

b. se st

5s − te st

c. se st

5s 4 − te st

d. e st

5 − e st

e. 5 − est

18

____ 40. Find dydx


e x

y 2= 12 + e

y

a.ye x

12e x + 3y 2 ey

b.2e x + y 3 e

y

ye x

c.y

2 + y 3

d.2ye x

e x + yey

e.ye x

2e x + y 3 ey

____ 41. Find dydx


ln (20 + exy

) = y

a.y

1 − x

b.ye

xy

20 + exy

c. 1

20 + exy

(1 − x)d. x + y

e.ye

xy

20 + exy

(1 − x)

19

____ 42. Find the equation of the tangent line for (xy)2 + (xy) − x = 11 at the point (-11 ,0).

a. y = - 111

x − 1

b. y = -11x − 1c. y = -11x − 2

d. y = - 111

x + 1

e. y = - 111

x − 2

____ 43. Use logarithmic differentiation to find dydx

.

y = (x 3 + x) x 3 + 6

a. 3x 2 x 3 + 12 3x 2 + 1

x 3 + x+ x 2

2x 3 + 6

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜̃

b. 3x 2 + 1

x 3 + x+ 3x 2

2x 3 + 12

Ê

Ë


ˆ

¯

˜̃̃˜̃̃˜̃̃˜̃

c. (x 3 + x) x 3 + 6 1

x 3 + x+ 1

2 (x 3 + 6)

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

d. (x 3 + x) x 3 + 6 3x2 + 1

x 3 + x+ 3x2

2 (x 3 + 6)

Ê

Ë


ˆ

¯

˜̃̃˜̃̃˜̃̃˜̃

e. (3x 2 + 1) 3x 2 + 1x

+ 3x 2

2x 3 + 12

Ê

Ë


ˆ

¯

˜̃̃˜̃̃˜̃̃˜̃

20

____ 44. The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by

P = x0.8 y0.6

where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars).

Compute dydx

at a production level of 30,000 CDs per day and x = 104.

a. -759.27b. -771.39c. -787.72d. 771.39e. -792.93

____ 45. Find the exact location of all the absolute extrema of the function with domain (-5, ∞).

f(x)=x4 −12x3

a. (-9, –2187) - relative maximumb. (9, –2187) - relative minimumc. (9, 0) - absolute maximumd. (9, 2187) - absolute minimume. (9, –2187) - absolute minimum

____ 46. Find the exact location of all the relative and absolute extrema of the function.

f(x) = x 2 + 49

x 2 − 49; -61 ≤ x ≤ 61, x ≠ ± 7

a. (0, -1) - relative minimumb. (0, -1) - relative maximumc. (0, -49) - absolute minimumd. (0, 49) - absolute maximume. (0, -1) - absolute maximum

____ 47. Find the exact location of all the relative and absolute extrema of the function with domain (-∞, ∞).

f(x) = e -5x8

a. (0, 1) - absolute maximumb. (0, 8) - relative minimumc. (1, 0) - absolute maximumd. (1, 5) - absolute maximume. (0, 1) - absolute minimum

21

____ 48. Find the exact location of all the relative and absolute extrema of the function with domain (0, ∞ ).

f(x) = x ln x 3

a. ( 1e

, - 13e

) - relative minimum

b. ( 1e

, - 3e

) - absolute minimum

c. ( 3e

, - 13e


d. ( 1e

, - 3e

) - relative maximum

e. ( 1e

, 3e


____ 49. The graph of the derivative of a function f is shown. Determine the x-coordinates of all stationary and singular points of f. (Assume that f (x) is defined and continuous everywhere in [-10, 1].)

a. x = 9b. x = -1c. x = 3d. x = -4e. x = -3

____ 50. Maximize P =xy with 4x + 5y = 160.

a. P = 2,000b. P = 5c. P = 160d. P = 640e. P = 320

22

____ 51. Minimize S = x + y with xy = 16 and both x and y > 0.

a. S = 8b. S = 16c. S = 6d. S = 4e. S = –8

____ 52. Minimize F = x 2 + y 2 with x + 4y = 68.

a. F = 68b. F = 256c. F = 204d. F = 4e. F = 272

____ 53. For a rectangle with perimeter 8 to have the largest area, what dimensions should it have?

a. 2×1b. 2×3c. 1×3d. 4×4e. 2×2

____ 54. For a rectangle with area 81 to have the smallest perimeter, what dimensions should it have?

a. 8×10b. 81×1c. 9×8d. 9×10e. 9×9

____ 55. The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:

C(q) = 1,000 + 150q 2

where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. Government clean air subsidies amount to $750 per pound of pollutant removed. How many pounds of pollutant should the firm remove each day to minimize net cost (cost minus subsidy)?

a. 2.5 poundsb. 10 poundsc. 75 poundsd. 2 poundse. 5 pounds

23

____ 56. I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $5 per foot, while the fencing for the north and south sides costs only $3 per foot. I have a budget of $150 for the project. What is the largest area I can enclose?

a. 375 square feetb. 15 square feetc. 187.5 square feetd. 93.75 square feete. 150 square feet

____ 57. A packaging company is going to make closed boxes, with square bases, that hold 216 cubic centimeters. What are the dimensions of the box that can be built with the least material?

a. 12×12×1.5 cmb. 6×6×6 cmc. 1×1×216 cmd. 3×3×24 cme. 1.5×1.5×96 cm

____ 58. Calculate d 2 y

dx2.

y = -14x 2 + 11x

a. -28b. 28x

c. -7x3 + 5.5x2

d. -14x2 + 11x

e. -7x3 − 154x2

24


dx2.

y = 18x

a.d 2 y

dx2= - x2

18

b.d 2 y

dx2= - 18

x2

c.d 2 y

dx2= x3

18

d.d 2 y

dx2= 18

x3

e.d 2 y

dx2= 36

x3


dx2.

y = 5x -5 + 2 lnx

a. 150x7

b. 5

x7− 2

x

c. 125

x2− 1

x2

d. 150

x7+ 2

x2

e. 150

x7− 2

x2

25

____ 61. The position s of a point (in feet) is given as a function of time t (in seconds).

s = -11 + 2t − 10t2 ; t = 2

a. Find its acceleration as a function of t.b. Find its acceleration at the specified time.

a. a(t) = 24 ft/sec2, a(t = 2) = -24 ft/sec2

b. a(t) = 5 ft/sec2, a(t = 2) = 5 ft/sec2

c. a(t) = 20 ft/sec2, a(t = 2) = 20 ft/sec2

d. a(t) = -2 ft/sec2, a(t = 2) = 2 ft/sec2

e. a(t) = -20 ft/sec2, a(t = 2) = -20 ft/sec2

____ 62. The position s of a point (in feet) is given as a function of time t (in seconds).

s = 4116 t + 6t3 ; t = 49

a. Find its acceleration as a function of t.b. Find its acceleration at the specified time.

a. -1029t t + 36t ft/sec2 , 1,761 ft/sec2

b. - 2058t

+ 12t ft/sec2 , 1,764 ft/sec2

c. - 2058t t

+ 18t ft/sec2 , 1,761 ft/sec2

d. - 1029t t

+ 36t ft/sec2 , 1,761 ft/sec2

e. - 1029t

+ 18t ft/sec2 , 1,764 ft/sec2

26

____ 63. The graph of a function f(x) = x2 (x2 − 24) is given.

Find the coordinates of all points of inflection of this function (if any).

a. (0, 0)b. (0, 0), (- 24 , 0), ( 24 , 0)c. (-2, -80), (2, -80)d. (-2, 80), (2, -80)e. (- 12 , -144), ( 12 , -144)

____ 64. In 1965 the economist F.M. Scherer modeled the number, n, of patens produced by a firm as a function of the size, s, of the firm (measured in annual sales in millions of dollars). He came up with the following equation based on a study of 448 large firms.

n = -3.53 + 134.08s − 24.66s2 + 1.428s3

Find d 2 n

ds2

|||||s = 2

.

a. –27.18b. –30.18c. –32.18d. 17.14e. –35.18

27

____ 65. A company finds that the number of new products it develops per year depends on the size if its annual R&D budget, x (in thousands of dollars), according to the following formula.

n = -1 + 11x + 2x2 − 0.2x3

Find n"(2).

a. 1.6b. 6.6c. 2.6d. –2.4e. 4.6

Multiple ResponseIdentify one or more choices that best complete the statement or answer the question.

____ 66. Locate all maxima in the graph.

Select all correct answers.

a. (9, 9)b. (0, 0)c. (4, 0)d. (-6, -7)e. (-3, 6)

28

____ 67. Find the exact location of all relative and absolute extrema of the function f (x) = 6x2 + 24x + 1with domain [-6, 6].


a. (–6, 361) - absolute maximumb. (–2, –361) - relative minimumc. (–6, 73) - relative maximumd. (6, 361) - absolute maximume. (6, 73) - relative maximumf. (–2, –23) - absolute minimum


f(x) = x (x − 21), x ≥ 0


a. (7, 7 ) - relative minimumb. (0,0) - absolute maximumc. (7, -14 7 ) - absolute minimumd. (7, -14 7 ) - relative minimume. (0,0) - relative maximum


f(x) = x2 − 32x + 6


a. (–4, –8) - relative minimumb. (8, 16) - relative maximumc. (–8, –16) - relative minimumd. (–8, –16) - relative maximume. (–4, –8) - relative maximum

29

____ 70. Find the exact location of all absolute extrema of the function.

f(x) = x − 2

x2 + 32


a. (1, 0.0625) - relative minimumb. (8, 0.0625) - absolute maximumc. (0, –0.1250) - relative minimumd. (8, 0.0625) - absolute minimume. (–4, –0.1250) - absolute minimum

Numeric Response

71. The monthly sales of Sunny Electronics' new stereo system is given by S(x) = 30x − x2 hundred units per

month, x months after its introduction. The price Sunny charges is p(x) = 800 − x2 dollars per stereo system, x months after its introduction. The revenue Sunny earns then must be R(x) = 100p(x)S(x). Find the rate of change of revenue 10 months after introduction.

Please enter your answer in dollars/month without the units.

72. The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by

P = x0.8 y0.6

where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars).

Compute dydx

at a production level of 24,000 CDs per day and x = 94.

73. Maximize P = xyz with x + y = 12 and z + y = 12, and x, y, and z > 0.

74. The demand for rubies at Royal Ruby Retailers is given by

q = - 54

p + 100

where p is the price RRR charges (in dollars) and q is the number of rubies RRR sells per week. At what price should RRR sell its rubies to maximize its weekly revenue?

Please enter your answer in dollars without the units.

30

75. Calculate d 2 y

dx2.

y = -4x 2 + 3x

Matching

Calculate the derivatives of the functions.

Match each function with the corresponding derivative.

a. f(x) = (19x + 63)8

b. f(x) = (34x − 81)13

c. f(x) = (31x + 74)0.6

____ 76. f '(x) = 152(19x + 63)7

____ 77. f '(x) = 442(34x − 81)12

____ 78. f '(x) = 18.6(31x + 74)−0.4

Short Answer

79. Find the equation of the line tangent to the graph of the given function at the point x = 1.

f(x) = (x2 + 2) (x3 + x)

80. Use logarithmic differentiation to find dydx

.

y = x4x

81. Find the exact location of all relative and absolute extrema of the function f(x) = 8x2 + 80x + 1 with domain [-6, 6].

31

82. The graph of the derivative of a function f is shown. Determine the x-coordinates of all stationary and singular points of f. (Assume that f (x) is defined and continuous everywhere in [-10, 10].)

Please enter your answer in the form "x = a, x = b, ..." where a, b, ... are the x-coordinates of stationary or singular points of f.

83. Calculate the derivative of the function.

f(x)=(x2 + 4x)5

84. Calculate the derivative of the function.

f(x)= (4.5x−6)8 +(7.7x+4)5È

Î

ÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇

7

Please enter your answer as an expression.

85. Find the derivative of the following function.

f(x) = log 4 2x

86. Find the derivative of the function.

h (x) = ln (7x + 7) (-9x + 1)ÈÎÍÍÍ

˘˚˙̇̇

ID: A

1

Review for Test 2Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 2. ANS: D PTS: 1 3. ANS: A PTS: 1 4. ANS: E PTS: 1 5. ANS: A PTS: 1 6. ANS: A PTS: 1 7. ANS: C PTS: 1 8. ANS: C PTS: 1 9. ANS: D PTS: 1 10. ANS: C PTS: 1 11. ANS: E PTS: 1 12. ANS: D PTS: 1 13. ANS: E PTS: 1 14. ANS: D PTS: 1 15. ANS: C PTS: 1 16. ANS: C PTS: 1 17. ANS: B PTS: 1 18. ANS: C PTS: 1 19. ANS: E PTS: 1 20. ANS: E PTS: 1 21. ANS: C PTS: 1 22. ANS: C PTS: 1 23. ANS: E PTS: 1 24. ANS: D PTS: 1 25. ANS: C PTS: 1 26. ANS: D PTS: 1 27. ANS: D PTS: 1 28. ANS: A PTS: 1 29. ANS: C PTS: 1 30. ANS: B PTS: 1 31. ANS: D PTS: 1 32. ANS: A PTS: 1 33. ANS: A PTS: 1 34. ANS: D PTS: 1 35. ANS: A PTS: 1 36. ANS: C PTS: 1 37. ANS: C PTS: 1 38. ANS: B PTS: 1 39. ANS: C PTS: 1 40. ANS: E PTS: 1

ID: A

2

41. ANS: E PTS: 1 42. ANS: A PTS: 1 43. ANS: D PTS: 1 44. ANS: A PTS: 1 45. ANS: E PTS: 1 46. ANS: B PTS: 1 47. ANS: A PTS: 1 48. ANS: B PTS: 1 49. ANS: D PTS: 1 50. ANS: E PTS: 1 51. ANS: A PTS: 1 52. ANS: E PTS: 1 53. ANS: E PTS: 1 54. ANS: E PTS: 1 55. ANS: A PTS: 1 56. ANS: D PTS: 1 57. ANS: B PTS: 1 58. ANS: A PTS: 1 59. ANS: E PTS: 1 60. ANS: E PTS: 1 61. ANS: E PTS: 1 62. ANS: D PTS: 1 63. ANS: C PTS: 1 64. ANS: C PTS: 1 65. ANS: A PTS: 1

MULTIPLE RESPONSE

66. ANS: A, E PTS: 1 67. ANS: C, D, F PTS: 1 68. ANS: C, E PTS: 1 69. ANS: A, D PTS: 1 70. ANS: B, E PTS: 1

NUMERIC RESPONSE

71. ANS: 300,000

PTS: 1 72. ANS: -662.71

PTS: 1 73. ANS: 256

PTS: 1

ID: A

3

74. ANS: 40

PTS: 1 75. ANS: -8

PTS: 1

MATCHING

76. ANS: A PTS: 1 77. ANS: B PTS: 1 78. ANS: C PTS: 1

SHORT ANSWER

79. ANS: y = 16x − 10

PTS: 1 80. ANS:

4x4x (ln x + 1)

PTS: 1 81. ANS:

(-5, -199), (-6, -191), (6, 769)

PTS: 1 82. ANS:

x = 2

PTS: 1 83. ANS:

5(2x + 4) ⋅ (x2 + 4x)4

PTS: 1 84. ANS:

7((4.5x − 6)8 + (7.7x + 4)5 )6 ⋅ (36(4.5x − 6)7 + 38.5(7.7x + 4)4 )

PTS: 1 85. ANS:

1(x ⋅ ln(4))

PTS: 1

ID: A

4

86. ANS: 7

(7x + 7)+ -9

(-9x + 1)

PTS: 1

Documents

Review for Test 2 - Arizona State Universitychoi/MAT210/MAT210_test2_Review...____ 16. The Thoroughbred Bus Company finds that its monthly costs for one particular year were given