#### Question Details

Hi, I don't understand how to do numbers 2 and 3 they both have graphs associated with them so I attached the homework to this question!

huffmeister (kmh4546) ? HW13 ? yu ? (53675)

This print-out should have 20 questions.

Multiple-choice questions may continue on

the next column or page ? find all choices

before answering.

001 of f the x-axis and y-axis have been omitted,

but the point P = (1, 1) on the graph has

been included.

Use calculus to determine which of the following f could be. 10.0 points

1. f (x) = 10

1

? 5x + 3x2 ? x3

3

3 2. f (x) = 8

1

? 3x + x2 + x3

3

3 If f is the function whose graph is given by 6 1 4

1

3. f (x) = ? + 5x ? 3x2 + x3

3

3 4 1

2

4. f (x) = ? + 3x ? x2 ? x3

3

3 2 2 4 6 which of the following properties does f have?

A. local minimum at x = 4 , 5. f (x) = 1

14

? 3x ? x2 + x3

3

3 8

1

6. f (x) = ? + 3x + x2 ? x3

3

3 B. critical point at x = 2 .

003 10.0 points 1. both of them

2. neither of them A function y = f (x) is known to have the

following properties 3. B only (i) f (0) = 0, 4. A only (ii) f changes concavity at x = 0,

002 10.0 points In drawing the graph

P (iii) f ?? < 0 on (??, ?4), f ?? > 0 on (4, ?).

Which of the following could be the graph of

f when dashed lines indicate asymptotes?

5 1. 4

3

2

1

0

-1

-2

-3

-4

-5

-6 4

2

?4 ?2

?2

?4 2 4 huffmeister (kmh4546) ? HW13 ? yu ? (53675)

6

5

2. 4

3

2

1

0

-1

-2

-3

-4

-5

-6

5

3. 4

3

2

1

0

-1

-2

-3

-4

-5

-6 2 y

1. 4

2

?4 ?2

?2 2 4 x ?4

y

2.

4

x 2

?4 ?2

?2 2 4

y ?4 3. x 5 4. 4

3

2

1

0

-1

-2

-3

-4

-5

-6

5

5. 4

3

2

1

0

-1

-2

-3

-4

-5

-6 4

2

?4 ?2

?2 2 4 y

4. ?4

x

4

2

y

?4 ?2

?2 2 4 5. ?4

x

004 10.0 points Which of the following is the graph of

005

f (x) = 3x 2/3 ? 2x . 10.0 points huffmeister (kmh4546) ? HW13 ? yu ? (53675) 3 Which function could have

1. f has exactly two critical points and one

inflection point

2. f has exactly one critical point and two

inflection points

2

?

3 4

?

3 2? 3. f has exactly two critical points and two

inflection points

4. f has exactly three critical points and

two inflection points

5. f has exactly one critical point and one

inflection points as its graph on [ 0, 2?]?

1. f (x) = ?

2. f (x) = sin x

2 + cos x 007 sin x

cos x ? 2 10.0 points A function f is defined by 3. f (x) = ? sin x

4. f (x) = f (x) = 3(x ? 4)ex?3 + 3 . sin x

2 + cos x 5. f (x) = sin x

6. f (x) = Which of the following is the graph of f ? sin x

2 ? cos x

006 10.0 points A certain function f is known to have

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9 8

6

4

2

?6 ?4 ?2

?2 2 4 6 8 10 ?4

?6

?8 as its graph on (?8, 12). Based on this graph,

which of the following is a true statement

about the critical and inflection points of f ? 5

4

1.3

2

1

0

-1

-2

-3

-4

-5

5

4

2.3

2

1

0

-1

-2

-3

-4

-5 4

2

?2

?2 2 4 2 4 ?4 4

2

?2

?2

?4 huffmeister (kmh4546) ? HW13 ? yu ? (53675)

4 3.3 4 2

1

0

-1

-2

-3

-4

-5 2 4

4.3

2

1

0

-1

-2

-3

-4

-5

5

4

5.3

2

1

0

-1

-2

-3

-4

-5 2 ?2

?2 4 1. y1 : y2 : y3 : 2. y1 : y2 : y3 : 3. y1 : y2 : y3 : 4. y1 : y2 : y3 : 5. y1 : y2 : y3 : 6. y1 : y2 : y3 : 4 ?4

4

2

2 ?2

?2 4 009

?4 10.0 points Find the area of the largest rectangle that

can be inscribed in a semi-circle of radius 6. 4 1. Area = 39 sq. units 2 2. Area = 38 sq. units

2 ?2

?2 4

3. Area = 36 sq. units

4. Area = 37 sq. units ?4

008 5. Area = 35 sq. units 10.0 points Identify the graphs of

2 ?x2 y1 = x e , 2 ?2x2 y2 = x e 010 10.0 points 2 ?3x2 , y3 = x e What is the maximum value of the product

P = xy when in y = 2 ? 5x ? 1 2 1. maximum value = 1

5 2. maximum value = 7

20 3. maximum value = 2

5 by applying the First Derivative Test to

2 f (x) = x2 e?mx . 4. maximum value = ? 7

20 huffmeister (kmh4546) ? HW13 ? yu ? (53675)

5. maximum value = ? 2

5 1. max area = 100 sq.yards 6. maximum value = ? 1

5 2. max area = 98 sq.yards 011 10.0 points A rectangle is inscribed in a semi-circle of

diameter d as shown in 5 3. max area = 101 sq.yards

4. max area = 102 sq.yards

5. max area = 99 sq.yards

013 10.0 points The canvas wind shelter d

What is the largest area the rectangle can

have when d = 8?

1. Area = 14 sq. units

2. Area = 15 sq. units

3. Area = 17 sq. units

4. Area = 16 sq. units

5. Area = 18 sq. units

012 10.0 points is to be constructed for use on Padre Island

beaches. It is to have a back, two square

sides, and a top. If 150 square feet of canvas

are available, find the length of the shelter for

which the volume inside is maximized assuming all the canvas is used.

1. length = 7 feet

2. length = 9 feet A rectangular dog pound with three kennels

as shown in the figure 3. none of the other answers

4. length = 8 feet

5. length = 10 feet

014 10.0 points If P (x, y) is a point on the line

consists of a rectangular fenced area divided

by two partitions. Determine the maximum

possible area of this pound if 56 yards of chain

link fencing is available for its construction. 3x + y = 6

as shown in huffmeister (kmh4546) ? HW13 ? yu ? (53675) 6 2. maximum area = 5 sq. units

6 3. maximum area = 3 sq. units

4. maximum area = 4 sq. units P (x, y) 5. maximum area = 8 sq. units

016

2 (not drawn to scale), find the value of x when

P is closest to the origin.

1. x = 2 10.0 points Find an equation for the tangent line to the

graph of

f (x) = 4

1

+ 3x + x2 ? x3

3

3 having maximum slope.

1. None of these 2. x = 19

10 2. y + 4x = 1 3. x = 17

10 3. y = 4x ? 1 4. x = 8

5 4. y + 4x + 1 = 0

5. y = 4x + 1 9

5. x =

5 017

015 10.0 points A rectangle is inscribed between the x-axis

and the parabola y = 3 ? x2 as shown in the

figure 10.0 points A company manufacturing cars at plant A

in Detroit and plant B in St. Louis has found

that its total cost function is

C = x2 + 2y 2 + 2xy + 40x + 20y + 40

when x cars are produced at plant A and y at

plant B.

What production level at plant A should

the company set to minimize the costs of production when filling an order for 40 cars?

1. prod plant A = 50 Determine the maximum possible area of

the rectangle.

1. maximum area = 7 sq. units 2. prod plant A = 45

3. prod plant A = 35 huffmeister (kmh4546) ? HW13 ? yu ? (53675) 7 4. prod plant A = 40

5. prod plant A = 30

018 (x, y)

b 10.0 points A rancher wishes to build a fence to enclose

a 1800 square yard rectangular field. Along

one side the fence is to be made of heavy duty

material costing $15 per yard, while the remaining three sides are to be made of cheaper

material costing $5 per yard. Determine the

least cost, Cmin , of fencing for the rancher.

1. Cmin = $1180 a rectangle is constructed having one side on

the x-axis and the two upper corner points on

the graph of

y = 3e?8x 2. Cmin = $1200 2 +3 Determine the maximum possible area, Amax ,

of this rectangle. 3. Cmin = $1140

4. Cmin = $1120 1. Amax = 3 5

e 2 sq. units

2 5. Cmin = $1160 2. Amax = 2 ?7

e 2 sq. units

3 3. Amax = 2 7

e 2 sq. units

3 4. Amax = 3 ?5

e 2 sq. units

2 5. Amax = 3 7

e 2 sq. units

2 019 10.0 points A trailer rental agency rents 8 trailers per

day at a rate of $24 per day. It discovers that

for each $4 increase in rate, one fewer trailer

is rented. Determine the maximum income

the rental agency can obtain.

1. maximum income = $188

2. maximum income = $200

3. none of these

4. maximum income = $196

5. maximum income = $192

6. maximum income = $204

020 . 10.0 points As shown in the figure

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