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

| August 31, 2017

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

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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
?

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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.

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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.

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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.

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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
(

,

)

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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
(

,

)

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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, ∞)

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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
(

,

)

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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.

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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?
$

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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

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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

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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 =

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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 =

.

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