Deck 13: Section 3: Functions of Several Variables

Question 1

Find the first partial derivative for the function with respect to z.

A)
B)
C)
D)
E)

Answer 1

Question 2

For , evaluate at the point .

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B)
C)
D)
E)

Answer 2

Question 3

Suppose a pharmaceutical corporation has two plants that produce the same over-the-counter medicine. If and are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by . When and find the marginal revenue for plant 1.

A) 174
B) 172
C) 80
D) 124
E) 93

Answer 3

80

Question 4

For find all values of x and y such that and simultaneously.

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B)
C)
D)
E)

Question 5

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 6

Suppose a company manufactures two types of wood-burning stoves: a freestanding model and a fireplace-insert model. The cost function for producing x freestanding and y fireplace-insert stoves is . Find the marginal costs when and . Round your answer to the nearest integer.

A) 192
B) 234
C) 210
D) 402
E) 403

Question 7

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 8

For , evaluate at the point .

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D)
E)

Question 9

For , evaluate at the point .

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B)
C)
D)
E)

Question 10

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 11

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 12

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 13

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 14

For , find all values of x and y such that and simultaneously.

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B)
C)
D)
E)

Question 15

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 16

For , evaluate at the point .

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B)
C)
D)
E)

Question 17

For , evaluate at the point .

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B)
C)
D)
E)

Question 18

Find the partial derivative for the function .

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B)
C)
D)
E)

Question 19

Find the second partial derivative for the function with respect to x.

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B)
C)
D)
E)

Question 20

For find all values of x and y such that and simultaneously.

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B)
C)
D)
E)

Question 21

Suppose the utility function is a measure of the utility (or satisfaction) derived by a person from the consumption of two products x and y. Determine the marginal utility of product if the utility function is .

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B)
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D)
E)

Question 22

Suppose the utility function is a measure of the utility (or satisfaction) derived by a person from the consumption of two products x and y. Determine the marginal utility of product x if the utility function is .

A)
B)
C)
D)
E)

Question 23

Suppose the temperature at any point in a steel plate is where x and y are measured in meters. At the point find the rate of change of the temperature with respect to the distance moved along the plate in the direction of the x-axis. Round your answer to one decimal place.

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B)
C)
D)
E)