Question 1

If

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Question 2

Find the second partial derivatives of the function

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Question 3

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

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Question 4

Find the differential of the function.

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Question 5

Describe the level survaces of the function

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Question 6

Find the local maximum, and minimum value and saddle points of the function.

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Question 7

Use partial derivatives to find the implicit derivative

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Question 8

Find the first partial derivatives of the function.

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Question 9

Find the first partial derivatives of the function

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Question 10

Find the differential of the function

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Question 11

Use Lagrange multipliers to find the maximum and minimum values of the function  subject to the constraints

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Question 12

Find the gradient of

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Question 13

Find the equation of the normal line to the given surface at the specified point.

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Question 14

Determine where the function  is continuous.

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Question 15

The length l, width w and height h of a box change with time.At a certain instant the dimensions are  nd l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s.At that instant find the rates at which the surface area is changing.

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Question 16

Use implicit differentiation to find

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Question 17

Sketch the graph of the function

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Question 18

Find all the second partial derivatives.

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Question 19

Find the differential of the function

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Question 20

Find three positive numbers whose sum is  and whose product is a maximum.

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Quiz 14: Partial Derivatives

If

Find the second partial derivatives of the function

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Find the differential of the function.

Describe the level survaces of the function

Find the local maximum, and minimum value and saddle points of the function.

Use partial derivatives to find the implicit derivative

Find the first partial derivatives of the function.

Find the first partial derivatives of the function

Find the differential of the function

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints

Find the gradient of

Find the equation of the normal line to the given surface at the specified point.

Determine where the function is continuous.

The length l, width w and height h of a box change with time.At a certain instant the dimensions are nd l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s.At that instant find the rates at which the surface area is changing.

Use implicit differentiation to find

Sketch the graph of the function

Find all the second partial derivatives.

Find the differential of the function

Find three positive numbers whose sum is and whose product is a maximum.