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Jul 16, 2020

MA16010 Exam 2 Practice Questions

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If h(t) = sin(3t) + cos(3t), find h(3)(t).

1.A© 27 sin(3t) + 27 cos(3t)

B© −27 sin(3t)− 27 cos(3t)

C© 27 sin(3t)− 27 cos(3t)

D© −27 sin(3t) + 27 cos(3t)

E© sin(3t)− cos(3t)

F© sin(3t) + cos(3t)

A toy rocket is launched from a platform on earth and flies straight up into the air. Its height during the first 10 seconds after launching is given by: s(t) = t3 + 3t2 + 4t + 100, where s is measured in centimeters, and t is in seconds. Find the velocity when the acceleration is 18 cm/s2.

2.A© 44 cm/s

B© 2 cm/s

C© 28 cm/s

D© 16 cm/s

E© 32 cm/s

F© 13 cm/s

MA16010 Exam 2 Practice Questions

Find dy

dx by implicit differentiation.

ln(xy) + 2x = ey

3.A© dy dx

= −2− y x− ey

B© dy dx

= −2y

1− yey

C© dy dx

= −2xy − y x− xyey

D© dy dx

= 1 + 2xy

xyey

E© dy dx

= −xy − y

2x− xyey

F© dy dx

= yey − y x − 2y

Find the critical numbers of y = x2ex.

4.A© −2 and 0

B© 0 and 2

C© 1 and 2

D© 0 and 1

E© −2 and 2

F© -2 and 1

MA16010 Exam 2 Practice Questions

Given f(x) = 2(3−x2)√

3x2 + 1 . Find f ′(1).

5.A© −7 2

B© −1 2

C© −13 6

D© −3 2

E© −9 4

F© −3 4

Find the largest open interval where g(t) is increasing.

g(t) = −1 3 t3 +

3

2 t2

6.A© (−∞, 0)

B© (0,∞)

C© (−∞, 3)

D© (0, 3)

E© (3,∞)

F© (−∞, 0) and (3,∞)

MA16010 Exam 2 Practice Questions

A spherical balloon is inflated with gas at a rate of 5 cubic centimeters per minute. How fast is the radius of the balloon changing at the instant when the radius is 4 centimeters?

The volume V of a sphere with a radius r is V = 4

3 πr3.

7.A© 5π 64

centimeters per minute

B© 5 4π

centimeters per minute

C© 5 16π

centimeters per minute

D© 5 64π

centimeters per minute

E© 256π 3

centimeters per minute

F© 25 4π

centimeters per minute

Find f ′(2).

f(t) = 2t− 1

(2t+ 1)2

8.A© 22125

B© − 2125

C© − 110

D© 2125

E© − 225

F© 4124

If y = ( 2x−12x+1 ) 3, then dy

dx =

9.A© 12(2x−1) 2

(2x+1)3

B© 48 (2x+1)4

C© 12(2x−1) 2

(2x+1)4

D© 3( 2x−12x+1 )2

E© 24x−12(2x+1)3

F© 6(2x−1) 2

(2x+1)3

MA16010 Exam 2 Practice Questions

Given f(x) = e5x ln(7x+ e). Find f ′(0).

10.A© 35 e

B© 1 + 7 e

C© 1 e

D© 5 + 7 e

E© 5 e

F© 1 + 1 e

The price of a commodity is given by p(t) = (t2 + 2t)2 + 100000, where p(t) is the price in dollars and t is years after 2000. At what rate is the price changing in the year of 2010?

11.A© $5280/year

B© $900/year

C© $2640/year

D© $4800/year

E© $2400/year

F© $1680/year

Find g′(x) if g(x) = tan2(3x2 + 2).

12.A© 6x tan(3x2 + 2) sec2(3x2 + 2)

B© 12x tan(3x2 + 2) sec2(3x2 + 2)

C© 12x sec2(3x2 + 2)

D© 2 sec2(6x)

E© 2 tan(6x)

F© 12x tan(3x2 + 2)

MA16010 Exam 2 Practice Questions

Use implicit differentiation to find dy dx

if x2 + y2 = 2xy + 5.

13.A© 2x− 2y − 5 2x− 2y

B© x x−y

C© 2y − 2x+ 5 2y − 2x

D© 1

E© 0

F© x 1−y

All edges of a cube are expanding at a rate of 2 centimeters per second. How fast is the surface area changing when each edge is 3 centimeters?

14.A© 36 cm2/sec

B© 12 cm2/sec

C© 72 cm2/sec

D© 48 cm2/sec

E© 54 cm2/sec

F© 46 cm2/sec

Water flows into a right cylindrical shaped swimming pool with a circular base at a rate of 4 m3/min. The radius of the base is 3 m. How fast is the water level rising inside the swimming pool? The volume of a right cylinder with a circular base is V = πr2h, where r is the radius of the base and h is the height of the cylinder.

15.A© 29π m/min

B© 49π m/min

C© 23π m/min

D© 43π m/min

E© 316π m/min

F© 38π m/min

MA16010 Exam 2 Practice Questions

A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?

16.A© 14 ft/sec

B© 8 ft/sec

C© 4 ft/sec

D© −3 ft/sec

E© − 13 ft/sec

F© −34 ft/sec

Given f(x) = sin3(2x), find f ′( π12 ).

17.A© − 3 √

3 8

B© 12

C© − √

3 4

D© 3 √

3 4

E© 32

F© 94

Given f(x) = ln 3 √

3 + 3x

3− x , find f ′(1).

18.A© 13

B© 23

C© 12

D© 16

E© 14

F© 18

MA16010 Exam 2 Practice Questions

Use implicit differentiation to find the equation of the tangent line to the graph at (−2, 2).

x2 + xy = 4− y2

19.A© y = 2

B© y = −x+ 4

C© y = x+ 2

D© y = x+ 4

E© y = −x+ 2

F© y = −x

Find dy dx

by implicit differentiation.

exy = 8x− 8y

20.A© dy dx

= 8− xexy 8 + yexy

B© dy dx

= 8

8 + xexy

C© dy dx

= 8 + yexy

8− xexy

D© dy dx

= 8

8− xexy

E© dy dx

= 8− yexy 8 + xexy

F© dy dx

= 8 + xexy

8− yexy

The position of an object moving on a straight line is given by s(t) = 48 − 3t − 2t2 − 6t3, where t is in minutes and s(t) is in meters. What is the acceleration when t = 3 minutes?

21.A© -177 m/min2

B© -114 m/min2

C© -110 m/min2

D© -112 m/min2

E© -108 m/min2

F© -76 m/min2

MA16010 Exam 2 Practice Questions

The sides of an equilateral triangle are expanding at a rate of 2 cm per minute. Find the rate of change of the area

when the length of each side is 3 cm. Use the fact that the area of an equilateral triangle is A = √

3 4 x

2 , where x is the length of a side.

22.A© 9 √

3 4 cm

2/min

B© √

3 cm2/min

C© 3 √

3 2 cm

2/min

D© 3 √

3 4 cm

2/min

E© 3 √

3 cm2/min

F© 9 √

3 2 cm

2/min

Given f(x) = x3

3 + x+

√ x3. Find f ′′(4).

23.A© 496

B© 498

C© 192

D© 678

E© 354

F© 263

Given y = x ln x, find y′′(e).

24.A© 0

B© 1 e

C© 2

D© 1 e

+ 1

E© e+ 1

F© e

MA16010 Exam 2 Practice Questions

Find the relative extrema of g(x) = x

x2 + 9 .

25.A© Relative maximum at x = √

3; Relative minimum at x = − √

3

B© Relative maximum at x = 3; Relative minimum at x = −3

C© Relative maximum at x = 3; Relative minimum at x = − √

3

D© Relative maximum at x = − √

3; Relative minimum at x = √

3

E© Relative maximum at x = −3; Relative minimum at x = √

3

F© Relative maximum at x = −3; Relative minimum at x = 3

Find the largest open interval(s) on which f(x) = (3x− 4)(x+ 2)

is increasing.

26.A© (− 13 ,∞)

B© (−∞, 3)

C© (−∞, 3) and (3,∞)

D© (−∞,− 13 )

E© (−∞,−2) and (43 ,∞)

F© (−2, 43 )

If x and y are both functions of t and x+ y2 = 4ex,

find dy dt

when dx dt

= 2, x = 0, and y = −2.

27.A© 1

B© − 32

C© 0

D© −1

E© − 12

F© 3

MA16010 Exam 2 Practice Questions

Find g′(1).

g(x) =

(

x2

x+ 2

)3

28.A© 13

B© 527

C© 53

D© 2527

E© 59

F© 253

The position of a particle on a straight line t seconds after it starts moving is s(t) = 2t3 − 3t2 + 6t+ 1 feet. Find the acceleration of the particle when its velocity is 78 ft/sec.

29.A© 46 ft/sec2

B© 30 ft/sec2

C© 84 ft/sec2

D© 42 ft/sec2

E© 105 ft/sec2

F© 258 ft/sec2

Find the relative maximum of f(x) = 2x3 − 6x.

30.A© (−1, 0)

B© (1,−4)

C© (1, 4)

D© (1, 0)

E© (0, 0)

F© (−1, 4)

MA16010 Exam 2 Practice Questions

Given that y2x− x2 = y ln(x) + 3,

use implicit differentiation to find dydx at (1,−2).

31.A© − 25

B© 5

C© 1

D© −2

E© 2

F© −1

Find f ′(4) if f(x) = (x2 + 3) √ x2 − 7.

32.A© 1103

B© 1636

C© 323

D© 1483

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