Question 1

How many critical points does the function f(x,y)=   + xy - 2  
- ln x - ln y have?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
E)  4 
A)  0 
B)  1 
C)  2 
D)  3 
E)  4

Question 2

The number of critical points of f(x,y)=   + 3  
+ 3  
- 15x + 2 is

Accepted Answer

A)  0. 
B)  1. 
C)  2. 
D)  3. 
E)  4. 
A)  0. 
B)  1. 
C)  2. 
D)  3. 
E)  4.

Question 3

A company's production function is given by P = 2.1   
   
,where P is the total output generated by L units of labor and k units of capital.Determine:
(a)the marginal production function with respect to L
(b)the marginal production function with respect to k

Accepted Answer

(a)1.26 @#IMG-DLM&_TB6578_11 @#IMG-DLM&_

Question 4

If f(x,y)=   ,then  
(x,y)=

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 5

The Cobb-Douglas production function for a company is given by P(l,k)= 70   
   
,where P is the monthly production value when k is the amount of the company's capital investment (in dollars per month)and l is the size of the labor force (in work hours per month).Find   
   
and   
   
.

Accepted Answer

@#IMG-DLM&_TB6578_11 @#IMG-DLM&_TB6578_1

Question 6

Use the method of Lagrange multipliers to determine the critical points of f(x,y,z)=   
- 3   
-   
+ 6 subject to the constraint 5x - 3y + z = 21.

Accepted Answer

The answer of Use the method of Lagrange multipliers to...

Question 7

A sporting goods store determines that the optimal quantity of athletic shoes (in pairs)to order each month is given by the Wilson lot size formula: Q(C,M,s)=   
,where C is the cost (in dollars)of placing an order,M is the number of pairs sold each month,and s is the monthly storage cost (in dollars)per pair of shoes.Find   
.Then find and interpret   
   
.

Accepted Answer

@#IMG-DLM&_TB6578_11 = @#IMG-DLM&_TB6578_11 ; @#IMG-DLM&_TB6

Question 8

For the joint-cost function c = 5xy   
+ 8000 (in $),determine the marginal costs   
and   
when   
and y = 5.

Accepted Answer

@#IMG-DLM&_TB6578_11 @#IMG-DLM&_TB6578_1

Question 9

Determine the critical points of f(x,y)= 2xy - 3x - y -   
- 3   
and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

Accepted Answer

@#IMG-DLM&_TB6578_11

Question 10

For the production function P = 6   
+ 5   
k + 6l   
+   
,find the marginal productivity functions   
and   
.

Accepted Answer

@#IMG-DLM&_TB6578_11 = 18 @#IMG-DLM&_TB6

Question 11

If f(x,y)=   
find

Accepted Answer

@#IMG-DLM&_TB6578_11

Question 12

Determine the critical points of f(x,y)=   
+ 2xy + 2   
- 4y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

Accepted Answer

@#IMG-DLM&_TB6578_11

Question 13

Find   
and   
where f(x,y)=   
   
+   
ln 3x and evaluate both derivatives at

Accepted Answer

3 @#IMG-DLM&_TB6578_11 @#IMG-DLM&_TB6578

Question 14

Evaluate:

Accepted Answer

The answer of Evaluate:  ...

Question 15

Determine the critical points of f(x,y)= 4   
+ 2x -   
+ 2y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

Accepted Answer

The answer of Determine the critical points of f(x,y)= 4...

Question 16

An empirical formula relating the surface area A (in square inches)of an average human body to the weight w (in pounds)and the height h (in inches)of the person is A(w,h)= 15.64   
   
.
Find   
   
and   
   
.

Accepted Answer

@#IMG-DLM&_TB6578_11 @#IMG-DLM&_TB6578_1

Question 17

A manufacturer of widgets has determined that the production function for a weekly production of p thousand gross of widgets is p = 1000 + 20   
   
- 5   
- 3   
,where l is the number of labor hours per week in thousands and k is the amount of capital in thousands of dollars per week.Determine both of the marginal productivity functions.

Accepted Answer

@#IMG-DLM&_TB6578_11 = 40 @#IMG-DLM&_TB6

Question 18

A critical point of f(x,y)= 2   + 3  
+ 7 subject to the constraint 2x - 5y = 31 is

Accepted Answer

A)  (2, 3) 
B)  (3, -5) 
C)  (-4, 1) 
D)    
E)  (0, 0) 
A)  (2, 3) 
B)  (3, -5) 
C)  (-4, 1) 
D)    
E)  (0, 0)

Question 19

The number of critical points of f(x,y)=   +  
Y +  
- 2y + 2 is

Accepted Answer

A)  0. 
B)  1. 
C)  2. 
D)  3. 
E)  4. 
A)  0. 
B)  1. 
C)  2. 
D)  3. 
E)  4.

Question 20

Evaluate:

Accepted Answer

A)    
B)    
C)  1 
D)    
E)    
A)    
B)    
C)  1 
D)    
E)

How many critical points does the function f(x,y)= + xy - 2 - ln x - ln y have?

The number of critical points of f(x,y)= + 3 + 3 - 15x + 2 is

A company's production function is given by P = 2.1 ,where P is the total output generated by L units of labor and k units of capital.Determine: (a)the marginal production function with respect to L (b)the marginal production function with respect to k

If f(x,y)= ,then (x,y)=

The Cobb-Douglas production function for a company is given by P(l,k)= 70 ,where P is the monthly production value when k is the amount of the company's capital investment (in dollars per month)and l is the size of the labor force (in work hours per month).Find and .

Use the method of Lagrange multipliers to determine the critical points of f(x,y,z)= - 3 - + 6 subject to the constraint 5x - 3y + z = 21.

For the joint-cost function c = 5xy + 8000 (in $),determine the marginal costs and when and y = 5.

Determine the critical points of f(x,y)= 2xy - 3x - y - - 3 and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

For the production function P = 6 + 5 k + 6l + ,find the marginal productivity functions and .

If f(x,y)= find

Determine the critical points of f(x,y)= + 2xy + 2 - 4y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

Find and where f(x,y)= + ln 3x and evaluate both derivatives at

Evaluate:

Determine the critical points of f(x,y)= 4 + 2x - + 2y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

An empirical formula relating the surface area A (in square inches)of an average human body to the weight w (in pounds)and the height h (in inches)of the person is A(w,h)= 15.64 . Find and .

A critical point of f(x,y)= 2 + 3 + 7 subject to the constraint 2x - 5y = 31 is

The number of critical points of f(x,y)= + Y + - 2y + 2 is

Evaluate:

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Exam 18: Multivariable Calculus

How many critical points does the function f(x,y)= + xy - 2 - ln x - ln y have?

The number of critical points of f(x,y)= + 3 + 3 - 15x + 2 is

A company's production function is given by P = 2.1 ,where P is the total output generated by L units of labor and k units of capital.Determine: (a)the marginal production function with respect to L (b)the marginal production function with respect to k

If f(x,y)= ,then (x,y)=

The Cobb-Douglas production function for a company is given by P(l,k)= 70 ,where P is the monthly production value when k is the amount of the company's capital investment (in dollars per month)and l is the size of the labor force (in work hours per month).Find and .

Use the method of Lagrange multipliers to determine the critical points of f(x,y,z)= - 3 - + 6 subject to the constraint 5x - 3y + z = 21.

For the joint-cost function c = 5xy + 8000 (in $),determine the marginal costs and when and y = 5.

Determine the critical points of f(x,y)= 2xy - 3x - y - - 3 and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

For the production function P = 6 + 5 k + 6l + ,find the marginal productivity functions and .

If f(x,y)= find

Determine the critical points of f(x,y)= + 2xy + 2 - 4y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

Find and where f(x,y)= + ln 3x and evaluate both derivatives at

Evaluate:

Determine the critical points of f(x,y)= 4 + 2x - + 2y and also determine by the second-derivative test whether each point corresponds to a relative maximum,to a relative minimum,to neither,or whether the test gives no information.

An empirical formula relating the surface area A (in square inches)of an average human body to the weight w (in pounds)and the height h (in inches)of the person is A(w,h)= 15.64 . Find and .

A critical point of f(x,y)= 2 + 3 + 7 subject to the constraint 2x - 5y = 31 is

The number of critical points of f(x,y)= + Y + - 2y + 2 is

Evaluate:

Review of Algebra

Applications and More Algebra

Functions and Graphs

Lines parabolas and Systems

Exponential and Logarithmic Functions

Mathematics of Finance

Matrix Algebra

Linear Programming

Introduction to Probability and Statistics

Additional Topics in Probability

Limits and Continuity

Differentiation

Additional Differentiation Topics

Curve Sketching

Integration

Methods and Applications of Integration

Continuous Random Variables

Filters