# Week 10 Assignment YINWEI LIU CED 6030, section 02, Fall 2015

Question

Week 10 Assignment

YINWEI LIU

CED 6030, section 02, Fall 2015

Instructor: He Wang

WebAssign

Week 10 Assignment (Homework)

Current Score : – / 118

Due : Wednesday, December 9 2015 11:59 PM EST

0/2 submissions

1. –/3 pointsLarApCalc8 3.1.002.MI.

Evaluate the derivative of the function at the indicated points on the graph. (If an answer is undefined, enter UNDEFINED.)

f ‘(1) =

f ‘(2) =

f ‘(4) =

4

f(x) = x + 2

x

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

1/16

12/3/2015

Week 10 Assignment

2. –/3 pointsLarApCalc8 3.1.004.

Consider the following function.

f (x) = 3x√x + 1

Evaluate the derivative of the function at the indicated points on the graph. (If an answer is undefined, enter UNDEFINED.)

f ‘ (1)

=

f ‘ (2/3) =

f ‘ (0)

=

3. –/16 pointsLarApCalc8 3.1.008.

Use the derivative to identify the open intervals on which the function is increasing or decreasing. Verify your result with the

graph of the function. (If you need to use or – , enter INFINITY or –INFINITY, respectively. Enter NONE in any unused

answer blanks.)

f (x) =

x2

x + 4

Increasing

?

,

?

and ?

?

,

?

and ?

,

?

Decreasing

?

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

2/16

12/3/2015

Week 10 Assignment

4. –/6 pointsLarApCalc8 3.1.018.MI.

Find the critical numbers and the open intervals on which the function is increasing or decreasing.

f(x) =

9 − x2

Critical numbers:

x=

(smallest value)

x=

x=

(largest value)

Increasing:

(0, 3)

[3, 0]

[0, 3]

(0, 3]

(3, 0)

Decreasing:

(0, 3)

(0, 3]

[3, 0]

[0, 3]

(3, 0)

Then use a graphing utility to graph the function.

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

3/16

12/3/2015

Week 10 Assignment

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

4/16

12/3/2015

Week 10 Assignment

5. –/20 pointsLarApCalc8 3.1.030.

Consider the following.

f(x) = 1/4x^4 8 x^2

(a) Find the critical numbers. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

(smallest)

(largest)

(b) Find the open intervals on which the function is increasing or decreasing. (If you need to use or – , enter

INFINITY or –INFINITY, respectively. Enter NONE in any unused answer blanks.)

Increasing

?

,

?

and ?

,

?

,

?

and ?

,

?

Decreasing

?

(c) Select the graph of the function.

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

5/16

12/3/2015

Week 10 Assignment

6. –/20 pointsLarApCalc8 3.1.038.

Consider the following.

y = {(x^3 + 5 text( )x <= 0, x^2 + 8 x text( ) x > 0)

(a) Find the critical numbers. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

(smallest)

(largest)

(b) Find the open intervals on which the function is increasing or decreasing. (If you need to use or – , enter

INFINITY or –INFINITY, respectively. Enter NONE in any unused answer blanks.)

Increasing

?

,

?

and ?

,

?

,

?

and ?

,

?

Decreasing

?

(c) Select the graph of the function.

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

6/16

12/3/2015

Week 10 Assignment

7. –/4 pointsLarApCalc8 3.2.004.

Find all relative extrema of the function. (Enter NONE in any unused answer blanks.)

f(x) = –5×2 + 5x + 7

Relative maximum

(

,

)

Relative minimum

(

,

)

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

7/16

12/3/2015

Week 10 Assignment

8. –/5 pointsLarApCalc8 3.2.016.

Consider the following function.

f (x) = x +

36

x

Use a graphing utility to graph the function. Select the graph of the function.

Find all relative extrema of the function. (Enter NONE in any unused answer blanks.)

Relative maximum

(

,

)

Relative minimum

(

,

)

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

8/16

12/3/2015

Week 10 Assignment

9. –/4 pointsLarApCalc8 3.2.024.MI.

Find the absolute extrema of the function on the closed interval. (If an answer does not exist, enter DNE.)

f(x) = x3 − 48x, [0, 16]

Maximum (x, y) =

,

Minimum (x, y) =

,

10.–/4 pointsLarApCalc8 3.2.034.

Find the absolute extrema of the function on the closed interval. (Enter NONE in any unused answer blanks. Use 2 decimal

places.)

f(x) = 3.3×5 + 7×3 – 3.7x, [0, 1]

Minimum

(

,

)

,

)

Maximum

(

11.–/2 pointsLarApCalc8 3.3.002.MI.

Analytically find the open intervals on which the graph is concave upward and those on which it is concave downward.

y = −x3 + 3×2 − 2

Concave upward:

(−∞, −1)

(1, ∞)

(−∞, ∞)

never concave upward

(−∞, 1)

Concave downward:

never concave downward

(−∞, 1)

(−∞, ∞)

(−∞, −1)

(1, ∞)

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

9/16

12/3/2015

Week 10 Assignment

12.–/7 pointsLarApCalc8 3.3.040.

Consider the following function.

f(x) = x3 – 3x

Select the graph of the function.

Identify all relative extrema and points of inflection. (Enter NONE in any unused answer blanks.)

Relative maximum

(

,

)

Relative minimum

(

,

)

Point of inflection

(

,

)

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

10/16

12/3/2015

Week 10 Assignment

13.–/3 pointsLarApCalc8 3.3.078.

The spread of a virus can be modeled by the following function where N is the number of people infected (in hundreds) and t is

the time (in weeks).

N = –t3 + 6t2, 0 ≤ t ≤ 6

(a) What is the maximum number of people projected to be infected?

people (in hundreds)

(b) When will the virus be spreading most rapidly?

weeks

(c) Select the graph of the model.

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

11/16

12/3/2015

Week 10 Assignment

14.–/2 pointsLarApCalc8 3.4.006.

Find two positive numbers satisfying the given requirements.

The product is 192 and the sum of the first plus three times the second is a minimum.

(smaller number)

(larger number)

15.–/1 pointsLarApCalc8 3.5.008.

Find the number of units x that produces the minimum average cost per unit C in the given equation.

C = 0.05×3 + 59×2 + 1384

units

16.–/1 pointsLarApCalc8 3.5.010.

Find the price per unit p that produces the maximum profit P.

C = 0.5x + 400 (Cost Function)

p =

30

√x

(Demand Function)

$

17.–/1 pointsLarApCalc8 3.5.002.MI.

Find the number of units x that produces a maximum revenue R.

R = 60×2 − 0.05×3

x =

units

18.–/1 pointsLarApCalc8 3.5.021.

When a wholesaler sold a product at $35 per unit, sales were 400 units per week. After a price increase of $2, however, the

average number of units sold dropped to 385 per week.Assuming that the demand function is linear, what price per unit will

yield a maximum total revenue?

$

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

12/16

12/3/2015

Week 10 Assignment

19.–/2 pointsLarApCalc8 3.5.038.MI.

The demand for a car wash is x = 800 − 40p, where the current price is $3. Can revenue be increased by lowering the price

and thus attracting more customers? Use price elasticity of demand η to determine your answer. (Round your answer to three

decimal places.)

η =

Yes, because the demand is elastic.

Yes, because the demand is inelastic.

No, because the demand is elastic.

No, because the demand is inelastic.

20.–/1 pointsLarApCalc8 3.8.004.

Find the differential dy.

y =

x + 8

7x – 1

dy =

21.–/1 pointsLarApCalc8 3.8.028.MI.

A state game commission introduces 28 deer into newly acquired state game lands. The population N of the herd can be

modeled by

14(4 + 8t)

2 + 0.06t

where t is the time in years. Use differentials to approximate the change in the herd size from t = 8 to t = 9. (Round your

N =

answer to the nearest integer.)

deer

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

13/16

12/3/2015

Week 10 Assignment

22.–/1 pointsLarApCalc8 4.3.010.

Find the derivative of the function.

g(x) = 3e8√x

g ‘ (x) =

23.–/1 pointsLarApCalc8 4.3.030.

Find the second derivative.

f(x) = (5 + 6x)e–5x

f ”(x) =

24.–/3 pointsLarApCalc8 4.3.044.

The balance A (in dollars) in a savings account is given by the function below where t is measured in years.

A = 2500e0.03t

Find the rate at which the balance is changing at each of the following times. (Enter your answers to the nearest cent.)

(a) t = 1 year

$

per year

(b) t = 10 years

$

per year

(c) t = 50 years

$

per year

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

14/16

12/3/2015

Week 10 Assignment

25.–/1 pointsLarApCalc8 4.5.012.

Find the derivative of the function.

y = (ln(x2))5

y ‘ =

26.–/1 pointsLarApCalc8 4.5.024.

Find the derivative of the function.

4

f(x) = x4ln(ex )

f ‘(x) =

27.–/1 pointsLarApCalc8 4.5.026.

Find the derivative of the function.

f(x) = ln

(

9 + ex

9 – ex

)

f ‘(x) =

28.–/1 pointsLarApCalc8 4.5.056.

Find dy/dx implicitly.

8xy + ln(x2y) = 6

dy/dx =

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

15/16

12/3/2015

Week 10 Assignment

29.–/2 pointsLarApCalc8 4.5.080.

Consider the following demand function.

x =

450

ln(p2 + 5)

Find dx/dp for the demand function.

dx/dp =

Interpret this rate of change when the price is $20. (Enter your answer to 2 decimal places.)

When p = 20, dx/dp =

.

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12701517

**30 %**discount on an order above

**$ 100**

Use the following coupon code:

RESEARCH