Week 11 Assignment YINWEI LIU CED 6030, section 02, Fall 2015

| August 30, 2017

Question
12/11/2015

Week 11 Assignment
YINWEI LIU
CED 6030, section 02, Fall 2015
Instructor: He Wang

WebAssign
Week 11 Assignment (Homework)
Current Score : – / 50

Due : Tuesday, December 15 2015 11:59 PM EST

0/2 submissions

1. –/2 pointsLarApCalc8 7.4.002.MI.

Find the first partial derivatives with respect to x and with respect to y.
z = x6 − 6y

∂z
=
∂x

∂z
=
∂y

2. –/2 pointsLarApCalc8 7.4.006.

Find the first partial derivatives with respect to x and with respect to y.

=

∂z
∂x
=

∂z
∂y

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Week 11 Assignment

3. –/2 pointsLarApCalc8 7.4.008.

Find the first partial derivatives with respect to x and with respect to y.
f(x, y) =

xy
x2 – y2

fx (x, y) =

fy (x, y) =

4. –/2 pointsLarApCalc8 7.4.012.

Find the first partial derivatives with respect to x and with respect to y.
g(x, y) = ex/y
gx (x, y) =

gy (x, y) =

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Week 11 Assignment

5. –/2 pointsLarApCalc8 7.4.014.

Find the first partial derivatives with respect to x and with respect to y.
g(x, y) = ln(x5 − y5)
gx (x, y) =

gy (x, y) =

6. –/3 pointsLarApCalc8 7.4.034.

Evaluate wx, wy, and wz at the point.
Function
w =

Point

xy

(1, 2, 0)

x – y – z

wx(1, 2, 0) =

wy(1, 2, 0) =

wz(1, 2, 0) =

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Week 11 Assignment

7. –/4 pointsLarApCalc8 7.4.048.

Find the four second partial derivatives. Observe that the second mixed partials are equal.
z = y3 – 6xy2 – 1
=

∂2z
∂x2
=

∂2z
∂x∂y
=

∂2z
∂y∂x
=

∂2z
∂y2

8. –/4 pointsLarApCalc8 7.4.058.

Evaluate the second partial derivatives fxx, fxy, fyy, and fyx at the point.
Function

Point

f(x, y) = x2ey

(–2, 0)

fxx (–2, 0) =

fxy (–2, 0) =

fyy (–2, 0) =

fyx (–2, 0) =

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Week 11 Assignment

9. –/1 pointsLarApCalc8 7.5.022.

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the critical point (x0, y0).
fxx(x0, y0) = –3, fyy(x0, y0) = –8, fxy(x0, y0) = 2
relative maximum
relative minimum
saddle point
insufficient information

10.–/1 pointsLarApCalc8 7.5.024.MI.

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the critical point (x0, y0).
fxx(x0, y0) = 19, fyy(x0, y0) = 11, fxy(x0, y0) = 1
relative minimum
relative maximum
saddle point
insufficient information

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Week 11 Assignment

11.–/4 pointsLarApCalc8 7.5.050.MI.

In order to treat a certain bacterial infection, a combination of two drugs is being tested. Studies have
shown that the duration of the infection in laboratory tests can be modeled by the function shown below,
where x is the dosage in hundreds of milligrams of the first drug and y is the dosage in hundreds of
milligrams of the second drug.
D(x, y) = x2 + 2y2 − 14x − 22y + 2xy + 22
Determine the partial derivatives of D with respect to x and with respect to y.

Dx =

Dy =

Find the amount of each drug necessary to minimize the duration of the infection.
first drug

hundred mg

second drug

hundred mg

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Week 11 Assignment

12.–/11 pointsLarApCalc8 7.6.002.SBS.

Use Lagrange multipliers to find the given extremum. In each case, assume that x and y are positive.
(Round to the nearest thousandth.)
Objective Function

Constraint

Maximize f(x, y) = xy

3x + y = 36

STEP 1: Define a new function F(x,y,λ).
F(x,y,λ) =

– λ(

)
STEP 2: Set the partial derivatives of F with respect to x, y, and λ equal to 0.
Fx =

= 0
Fy =

= 0
Fλ =

= 0
STEP 3: Solve for λ, x, and y.
λ =
x =
y =
STEP 4: Find the maximum.
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Week 11 Assignment

f(

,

) =

13.–/3 pointsLarApCalc8 7.6.008.

Use Lagrange multipliers to find the given extremum. In each case, assume that x and y are positive.
(Round to the nearest thousandth.)
Objective Function
Minimize f(x, y) = 3x + y + 48
f(

Constraint
x2y = 6

,

) =

14.–/1 pointsLarApCalc8 5.1.010.

Find the indefinite integral and check your result by differentiation. (Use C for the constant of
integration.)

15.–/1 pointsLarApCalc8 5.1.014.

Find the indefinite integral and check your result by differentiation. (Use C for the constant of
integration.)

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Week 11 Assignment

16.–/1 pointsLarApCalc8 5.1.018.

Find the indefinite integral and check your result by differentiation. (Use C for the constant of
integration.)

17.–/1 pointsLarApCalc8 5.1.032.

Find the indefinite integral and check your result by differentiation. (Use C for the constant of
integration.)

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Week 11 Assignment

18.–/2 pointsLarApCalc8 5.4.002.

Consider the following integral.

(a) Select the graph of the integrand.

(b) Use the graph to determine whether the definite integral is one of the following.
negative
zero
positive

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Week 11 Assignment

19.–/2 pointsLarApCalc8 5.4.010.

Consider the following integral.

(a) Select the graph of the region whose area is represented by the definite integral.

(b) Use a geometric formula to evaluate the integral.

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20.–/1 pointsLarApCalc8 5.4.046.

Evaluate the definite integral. (Round to 2 decimal places.)

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