Question 1

Select the correct Answer: for each question.
-Use the equation

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Sketch the graph of the function

Accepted Answer

The answer of Sketch the graph of the function ...

Question 3

Find   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E) 0 
A)    
B)    
C)    
D)    
E) 0

Question 4

Determine the largest set on which the function is continuous.

Accepted Answer

The answer of Determine the largest set on which the...

Question 5

Select the correct Answer: for each question.
-Use the Chain Rule to find

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Accepted Answer

maximum =

Question 7

Select the correct Answer: for each question.
-Find the indicated partial derivative.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Select the correct Answer: for each question.
-Find and classify the relative extrema and saddle points of the function

Accepted Answer

A) None 
B)    Relative maximum 
C) Saddle point   Relative minimum 
D)    
A) None 
B)    Relative maximum 
C) Saddle point   Relative minimum 
D)

Question 9

Select the correct Answer: for each question.
-Find the indicated partial derivative.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

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

Accepted Answer

The answer of Find three positive numbers whose sum is...

Question 11

Use the Chain Rule to find

Accepted Answer

The answer of Use the Chain Rule to find ...

Question 12

Select the correct Answer: for each question.
-Use the Chain Rule to find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

At what point is the following function a local maximum?

Accepted Answer

The answer of At what point is the following function...

Question 14

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

Accepted Answer

The answer of Find the equation of the normal line...

Question 15

Find the absolute minimum value of the function   on the set D.D is the region bounded by the parabola   and the line   Select the correct Answer

Accepted Answer

A)    
B)    
C) 30 
D)    
E) 0 
A)    
B)    
C) 30 
D)    
E) 0

Question 16

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

Accepted Answer

The answer of Find the dimensions of a rectangular box...

Question 17

Let   Find   Select the correct Answer

Accepted Answer

A) 24 
B) 3/2 
C)    
D) 6 
A) 24 
B) 3/2 
C)    
D) 6

Question 18

Use the Chain Rule to find   Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 20

Select the correct Answer: for each question.
-Find the maximum rate of change of   at the point   In what direction does it occur?

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Select the correct Answer: for each question. -Use the equation

Sketch the graph of the function

Find Select the correct Answer

Determine the largest set on which the function is continuous.

Select the correct Answer: for each question. -Use the Chain Rule to find

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Select the correct Answer: for each question. -Find the indicated partial derivative.

Select the correct Answer: for each question. -Find and classify the relative extrema and saddle points of the function

Select the correct Answer: for each question. -Find the indicated partial derivative.

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

Use the Chain Rule to find

Select the correct Answer: for each question. -Use the Chain Rule to find

At what point is the following function a local maximum?

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

Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line Select the correct Answer

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

Let Find Select the correct Answer

Use the Chain Rule to find Select the correct Answer

Find the differential of the function.

Select the correct Answer: for each question. -Find the maximum rate of change of at the point In what direction does it occur?

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 14: Partial Derivatives

Select the correct Answer: for each question. -Use the equation

Sketch the graph of the function

Find Select the correct Answer

Determine the largest set on which the function is continuous.

Select the correct Answer: for each question. -Use the Chain Rule to find

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Select the correct Answer: for each question. -Find the indicated partial derivative.

Select the correct Answer: for each question. -Find and classify the relative extrema and saddle points of the function

Select the correct Answer: for each question. -Find the indicated partial derivative.

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

Use the Chain Rule to find

Select the correct Answer: for each question. -Use the Chain Rule to find

At what point is the following function a local maximum?

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

Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line Select the correct Answer

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

Let Find Select the correct Answer

Use the Chain Rule to find Select the correct Answer

Find the differential of the function.

Select the correct Answer: for each question. -Find the maximum rate of change of at the point In what direction does it occur?

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters