33.Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is maximum.Answers

A.

28 and 28

B.

28 and 14

C.

22 and 17

D.

34 and 11

E.

24 and 16

35.Find the length and width of a rectangle that has an area of 968 square feet and whose perimeter is a minimum.Answers

A.

l= 242 feet;w= 4 feet

B.

l=w= 22feet

C.

l= 484 feet;w= 2 feet

D.

l= 121 feet;w= 8 feet

E.

l= 484feet;w=feet

37.A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 23 cm³. Find the radius, r, of the cylinder that produces the minimum surface area. Round your answer to two decimal places.Answers

A.

r 1.76 cm

B.

r 2.30 cm

C.

r 2.34 cm

D.

r 2.10 cm

E.

r 3.12 cm

Question38.Complete two iterations of Newton's Method for the function f(x) = x²- 7 using the initial guess 2.6. Round your answers to four decimal places.Answers

A.

2.6463, 2.6456

B.

2.6463, 2.6460

C.

2.6463, 2.6459

D.

2.6459, 2.6457

E.

2.6462, 2.6458

Question39.

Use Newton's Method to approximate the zero(s) of the function f(x) = x⁵+ 4x + 1 accurate to three decimal places.

Answers

A.

0.250

B.

0.250

C.

0.292

D.

0.281

E.

0.197

Question40.The linear approximation of f(x) = cos x for small values of x centered around x = 0 isAnswers

A.

f(x) = 1 + x.

B.

f(x) = 1 - x.

C.

f(x) = x.

D.

f(x) = 1.

E.

none of these.

41.Use differentials to approximate the value of, centering your linear approximation onx= 4.Answers

A.

2.125

B.

8.509

C.

9.850

D.

1.125

Question42.The edge of a cube is measured at 3 cm, with a possible measurement error of 0.2 cm. Use differentials to estimate the maximum possible propogated error in computing the volume of the cube.Answers

A.

0.08 cm³

B.

30.72 cm³

C.

32.768 cm³

D.

6.5536 cm³

E.

5.4 cm³

Question43.Locate the absolute extrema of the functionf(x) =x³- 12xon the closed interval [0, 4].Answers

A.

absolute max: (2, 16); absolute min: (4, 16)

B.

no absolute max; absolute min: (4, 16)

C.

absolute max: (4, 16); absolute min: (2, 16)

D.

absolute max: (4, 16); no absolute min

E.

no absolute max or min

45.Which of the following functions passes through the point (0, 10) and satisfiesf '(x) = 12.Answers

A.

f(x) = 10x+ 12

B.

f(x) =

C.

f(x) = 12x+ 10

D.

f(x) = 10x

E.

f(x) =+ 10

Question46.Find the relative extremum off(x) = 9x²+ 54x+ 2 by applying the First Derivative Test.Answers

A.

relative minimum: (4, 358)

B.

relative maximum: (3, 241)

C.

relative minimum: (4, 74)

D.

relative minimum: (2, 74)

E.

relative maximum: (3, 83)

48.A rectangular page is to contain 144 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.Answers

A.

25, 25

B.

16, 16

C.

15, 15

D.

14, 14

E.

13, 13

50.Find the equation of the tangent line T to the graph of f(x) = 8 sin x at the given point (6, 8 sin 6).Answers

A.

y = (8 sin 6)(x + 6) + 8 cos 6

B.

y = (8 cos 6)(x - 6) + 8 sin 6

C.

y = (8 cos 6x)(x - 6) + 8 sin 6

D.

y = (8 sin 6x)(x + 6) + 8 cos 6

E.

y = (8 cos 6)(x - 6) + 8 sin 6