Question 1

Find the points on the surface  that are closest to the origin.
A) 
B) 
C) 
D) 
E)

Accepted Answer

E

Question 2

Find and classify the relative extrema and saddle points of the function  .

Accepted Answer

Relative minimum  Saddle points  and

Question 3

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Accepted Answer

The answer of Use Lagrange multipliers to find the minimum...

Question 4

Use Lagrange multipliers to find the maximum value of the function subject to the given constraints.

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 5

Find the shortest distance from the point  to the plane  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the shortest distance from the point...

Question 6

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 7

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 8

Find the absolute minimum value of the function  on the set D. D is the region bounded by the parabola  and the line 
A)0
B) 
C) 
D) 
E)30

Accepted Answer

The answer of Find the absolute minimum value of the...

Question 9

Find three positive numbers whose sum is  and whose product is a maximum.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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

Question 10

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

B)4, 8, 16
C)32,  , 16
D)  ,  ,

E)32, 32, 32

Accepted Answer

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

Question 11

Find and classify the relative extrema and saddle points of the function  for  and  .
A)Relative maximum 
B)Saddle point 
C)Relative minimum 
D)None

Accepted Answer

The answer of Find and classify the relative extrema and...

Question 12

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of  ,  ,  what can you say about f ?
A)f has a saddle point at (1,1)
B)f has a local minimum at (1,1)
C)f has a local maximum at (1,1)

Accepted Answer

The answer of Suppose (1, 1) is a critical point...

Question 13

A cardboard box without a lid is to have a volume of  cm  . Find the dimensions that minimize the amount of cardboard used.

Accepted Answer

The answer of A cardboard box without a lid is...

Question 14

Find the absolute extrema of the function  on the closed triangular region with vertices  ,  and  .
A)Absolute minimum 5, Absolute maximum 17
B)Absolute minimum 0, Absolute maximum 5
C)Absolute minimum -5, Absolute maximum 5
D)Absolute minimum -5, Absolute maximum 17

Accepted Answer

The answer of Find the absolute extrema of the function...

Question 15

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

Accepted Answer

The answer of Find the local maximum, and minimum value...

Question 16

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

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 17

Find the dimensions of the rectangular box with largest volume if the total surface area is given as   .
A)  cm,  cm, 1.75 cm
B)  cm, 1.75 cm, 1.75 cm
C)  cm,  cm,
 cm
D)  cm,  cm,
 cm
E)  cm,  cm, 3.5 cm

Accepted Answer

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

Question 18

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 19

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

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 20

Find the critical points of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the critical points of the function....

Quiz 11: Partial Derivatives

Find the points on the surface that are closest to the origin.

Find and classify the relative extrema and saddle points of the function .

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Use Lagrange multipliers to find the maximum value of the function subject to the given constraints.

Find the shortest distance from the point to the plane .

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

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

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

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

Find and classify the relative extrema and saddle points of the function for and .

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of , , what can you say about f ?

A cardboard box without a lid is to have a volume of cm . Find the dimensions that minimize the amount of cardboard used.

Find the absolute extrema of the function on the closed triangular region with vertices , and .

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

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

Find the dimensions of the rectangular box with largest volume if the total surface area is given as .

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

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

Find the critical points of the function.