Question 1

If f(x)=   + 3  
- 24x + 8,then f is

Accepted Answer

A)  decreasing on (-∞, 4), concave up on (-1, ∞), and has no relative minimum point. 
B)  decreasing on (1, 2), concave up (0, ∞), and has a relative minimum when x = -4. 
C)  increasing on (2, ∞), concave up on (-∞, -1), and has a relative minimum when x = 2. 
D)  increasing on (-4, 2), concave down on (-∞, ∞), and has a relative maximum when x = 2. 
E)  decreasing on (-4, 2), concave down on (-∞, -1), and has a relative maximum when x = -4. 
A)  decreasing on (-∞, 4), concave up on (-1, ∞), and has no relative minimum point. 
B)  decreasing on (1, 2), concave up (0, ∞), and has a relative minimum when x = -4. 
C)  increasing on (2, ∞), concave up on (-∞, -1), and has a relative minimum when x = 2. 
D)  increasing on (-4, 2), concave down on (-∞, ∞), and has a relative maximum when x = 2. 
E)  decreasing on (-4, 2), concave down on (-∞, -1), and has a relative maximum when x = -4.

Question 2

The demand equation for a monopolist's product is p = 200 - 0.98q,where p is the price per unit (in dollars)of producing q units.If the total cost c (in dollars)of producing 8 units is given by   
find the level of production at which profit is maximized.

Accepted Answer

The answer of The demand equation for a monopolist's product...

Question 3

Here is a function and its first and second derivatives:
f(x)=   
f'(x)=   
f''(x)=   
(a)Determine all x- and y-intercepts.
(b)Determine equations of all vertical asymptotes and non-vertical asymptotes.
(c)Determine intervals on which the function is increasing; determine intervals on which the function is decreasing.
(d)Determine the coordinates of all relative maximum and relative minimum points.
(e)Determine intervals on which the function is concave up; determine intervals on which the function is concave down.
(f)Determine the coordinates of all inflection points.
(g)With the aid of the information obtained in parts (a)- (g),give a reasonable sketch of the curve.

Accepted Answer

(a)(0,0)
(b)x = 2
(c)inc.on (-

Question 4

Sketch the graph of y =   
- 7x with the aid of intercepts,symmetry,and the first-derivative test.Use your graphing calculator to verify your solution.

Accepted Answer

The answer of Sketch the graph of y = ...

Question 5

Find all the critical values of f(x)=   
.

Accepted Answer

The answer of Find all the critical values of f(x)=...

Question 6

A released film has a revenue given by R(t)=   
,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

Accepted Answer

The answer of A released film has a revenue given...

Question 7

The function y =   +  
+ x - 3 has how may inflection points?

Accepted Answer

A)  none 
B)  one 
C)  two 
D)  three 
E)  four 
A)  none 
B)  one 
C)  two 
D)  three 
E)  four

Question 8

Find all the critical values of f(x)= x ln x.

Accepted Answer

The answer of Find all the critical values of f(x)=...

Question 9

The function f(x)= 4   - 10  
- 8x + 3 is decreasing on

Accepted Answer

A)    
B)    
C)  (2, ∞) 
D)    
E)  (-∞, 2). 
A)    
B)    
C)  (2, ∞) 
D)    
E)  (-∞, 2).

Question 10

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima.
f(x)= (   
- 3x +

Accepted Answer

Increasing on the intervals @#IMG-DLM&_T

Question 11

Find two numbers whose sum is 30 and whose product is a maximum.

Accepted Answer

The answer of Find two numbers whose sum is 30...

Question 12

On the interval   ,the function y = 4 +  
-  
Has an absolute maximum when x =

Accepted Answer

A)  0. 
B)  1. 
C)  -1. 
D)    
E)  -   
A)  0. 
B)  1. 
C)  -1. 
D)    
E)  -

Question 13

Let y = 3   
   
(a)Find y' and y''.
(b)Determine intervals on which the function is increasing; determine intervals on which the function is decreasing.
(c)Determine the coordinates of all relative maximum and relative minimum points.
(d)Determine intervals on which the function is concave up; determine intervals on which the function is concave down.
(e)Determine the coordinates of all inflection points.
(f)With the aid of the information obtained in parts (a)- (e),give a reasonable sketch of the curve.

Accepted Answer

(a)Find y' = 6 @#IMG-DLM&_TB6578_11 @#IMG-DLM&_TB6578_11 + 6

Question 14

Find the intervals where the graph of y = f(x)is concave up and where it is concave down.Do not sketch its graph.Also determine its points of inflection.f(x)=   
-   
.

Accepted Answer

Concave up on (-∞,0)

Question 15

A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the enclosed area.If 2000 ft of fencing are to be used,find the maximum area that can be enclosed.Assume the answer is in square feet.

Accepted Answer

A)  400,000 
B)  500,000 
C)  600,000 
D)  700,000 
E)  800,000 
A)  400,000 
B)  500,000 
C)  600,000 
D)  700,000 
E)  800,000

Question 16

Determine the equations of the vertical asymptotes and non-vertical asymptotes for the graph of

Accepted Answer

horiz.asym.y = @#IMG-DLM&_TB65

Question 17

Find all the critical values of f(x)=   
.

Accepted Answer

The answer of Find all the critical values of f(x)=...

Question 18

Let y =   
(a)Determine all x- and y- intercepts.
(b)Determine equations of all vertical and non-vertical asymptotes.
(c)Determine y' and y''.
(d)Determine intervals on which the function is increasing; determine intervals on which the function is decreasing.
(e)Determine the coordinates of all relative maximum and relative minimum points.
(f)Determine intervals on which the function is concave up; determine intervals on which the function is concave down.
(g)Determine the coordinates of all inflection points.
(h)With the aid of the information obtained in parts (a)- (g),give a reasonable sketch of the curve.

Accepted Answer

(a)x- and y-intercepts is (0,0)
(b)verti

Question 19

A released film has a revenue given by R(t)=   
,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

Accepted Answer

The answer of A released film has a revenue given...

Question 20

Find all the critical values of f(x)=   
.

Accepted Answer

The answer of Find all the critical values of f(x)=...

If f(x)= + 3 - 24x + 8,then f is

The demand equation for a monopolist's product is p = 200 - 0.98q,where p is the price per unit (in dollars)of producing q units.If the total cost c (in dollars)of producing 8 units is given by find the level of production at which profit is maximized.

Sketch the graph of y = - 7x with the aid of intercepts,symmetry,and the first-derivative test.Use your graphing calculator to verify your solution.

Find all the critical values of f(x)= .

A released film has a revenue given by R(t)= ,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

The function y = + + x - 3 has how may inflection points?

Find all the critical values of f(x)= x ln x.

The function f(x)= 4 - 10 - 8x + 3 is decreasing on

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima. f(x)= ( - 3x +

Find two numbers whose sum is 30 and whose product is a maximum.

On the interval ,the function y = 4 + - Has an absolute maximum when x =

Find the intervals where the graph of y = f(x)is concave up and where it is concave down.Do not sketch its graph.Also determine its points of inflection.f(x)= - .

A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the enclosed area.If 2000 ft of fencing are to be used,find the maximum area that can be enclosed.Assume the answer is in square feet.

Determine the equations of the vertical asymptotes and non-vertical asymptotes for the graph of

Find all the critical values of f(x)= .

A released film has a revenue given by R(t)= ,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

Find all the critical values of f(x)= .

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

Integration

Methods and Applications of Integration

Continuous Random Variables

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Exam 14: Curve Sketching

If f(x)= + 3 - 24x + 8,then f is

The demand equation for a monopolist's product is p = 200 - 0.98q,where p is the price per unit (in dollars)of producing q units.If the total cost c (in dollars)of producing 8 units is given by find the level of production at which profit is maximized.

Sketch the graph of y = - 7x with the aid of intercepts,symmetry,and the first-derivative test.Use your graphing calculator to verify your solution.

Find all the critical values of f(x)= .

A released film has a revenue given by R(t)= ,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

The function y = + + x - 3 has how may inflection points?

Find all the critical values of f(x)= x ln x.

The function f(x)= 4 - 10 - 8x + 3 is decreasing on

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima. f(x)= ( - 3x +

Find two numbers whose sum is 30 and whose product is a maximum.

On the interval ,the function y = 4 + - Has an absolute maximum when x =

Find the intervals where the graph of y = f(x)is concave up and where it is concave down.Do not sketch its graph.Also determine its points of inflection.f(x)= - .

A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the enclosed area.If 2000 ft of fencing are to be used,find the maximum area that can be enclosed.Assume the answer is in square feet.

Determine the equations of the vertical asymptotes and non-vertical asymptotes for the graph of

Find all the critical values of f(x)= .

A released film has a revenue given by R(t)= ,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

Find all the critical values of f(x)= .

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

Integration

Methods and Applications of Integration

Continuous Random Variables

Multivariable Calculus

Filters