Question 1

The function f(x)=   - 6x + 8 is decreasing on

Accepted Answer

A)  (3, ∞). 
B)  (-3, 3). 
C)  (2, 4). 
D)  (-∞, 2) and (4, ∞). 
E)  (-∞, 3). 
A)  (3, ∞). 
B)  (-3, 3). 
C)  (2, 4). 
D)  (-∞, 2) and (4, ∞). 
E)  (-∞, 3).

Question 2

Find the absolute extrema for y =   
+   
- 3x + 7 on the interval   
and where they occur.

Accepted Answer

absolute maximum at

Question 3

If f(x)=   + 2  
- 4x + 10,then f is

Accepted Answer

A)  decreasing on (-2, ∞), concave down on   , and has a relative maximum when x = -2. 
B)  decreasing on   , concave up on   , and has a relative minimum when x = -   
C)  increasing on   , concave down on   , and has a relative minimum when x = -2. 
D)  increasing on   , concave down on   , and has a relative maximum when x =   
E)  increasing on   , concave up on (-∞, ∞), and has a relative minimum when x = -2. 
A)  decreasing on (-2, ∞), concave down on   , and has a relative maximum when x = -2. 
B)  decreasing on   , concave up on   , and has a relative minimum when x = -   
C)  increasing on   , concave down on   , and has a relative minimum when x = -2. 
D)  increasing on   , concave down on   , and has a relative maximum when x =   
E)  increasing on   , concave up on (-∞, ∞), and has a relative minimum when x = -2.

Question 4

Find all the critical values of f(x)=   
- 2   
.

Accepted Answer

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

Question 5

The demand equation for a monopolist's product is p = 2700 -   
,where p is the price per unit (in dollars)when q units are demanded.
(a)Find the value of q for which revenue is maximum.
(b)What is the maximum revenue?

Accepted Answer

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

Question 6

If f(x)=   - 6  
+ 3,then f has an inflection point when x =

Accepted Answer

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

Question 7

A rectangular plot of ground is to be fenced in so that it has an area of 15,000 square feet.The plot is to be divided in half with a fence parallel to one pair of sides.Find the dimensions of the plot if the least amount of fencing is to be used.

Accepted Answer

The answer of A rectangular plot of ground is to...

Question 8

If y =   
+ 4   
- 3x + 4,use the second-derivative test to find all values of x for which (a)relative maxima occur (b)relative minima occur.

Accepted Answer

(a)-3 
(b)

Question 9

The revenue equation for a company is given by R(x)= 68.04x - 0.07   
.Determine when relative extrema occur on the interval (0,∞).

Accepted Answer

relative m

Question 10

Sensitivity to a drug depends on the dosage size x according to the equation s = 100x -   
.Find the dosage that maximizes sensitivity.

Accepted Answer

The answer of Sensitivity to a drug depends on the...

Question 11

An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.

Accepted Answer

The answer of An open box is to be made...

Question 12

Find all the critical values of f(x)=   
- 8   
+ 3.

Accepted Answer

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

Question 13

Let y =   
(a)Determine all x - and y-intercepts.
(b)Determine equations of all vertical asymptotes 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)(2,0),(0,4)
(b)y = 2,x = 1
(c) @#IMG-DLM&_TB657

Question 14

The graph of a function is given.Find
(a)the open intervals on which the function is increasing or decreasing;
(b)the coordinates of all relative extrema.

Accepted Answer

(a)f(x)is decreasing on (-∞,-3

Question 15

Find two numbers whose sum is 50 and such that the product of one of them and five more than the other is a maximum.

Accepted Answer

@#IMG-DLM&_TB6578_11

Question 16

On the interval   ,the function y =  
+ 3  
- 9x + 27 has an absolute maximum when x =

Accepted Answer

A)  2. 
B)  0. 
C)  1. 
D)    
E)  none of the above 
A)  2. 
B)  0. 
C)  1. 
D)    
E)  none of the above

Question 17

The profit equation for a taco stand is given by P(x)= -0.4   
+ 100x - 100,where x is the number of tacos sold,and P(x)is the profit in dollars.Use the first-derivative test to find when relative extrema occur.

Accepted Answer

There is a

Question 18

The cost equation for a cookie store is given by C(x)=   
- 6   
+ 250,where x is the number of cookies made (in dozens)and C(x)is the cost in dollars.Use the first-derivative test to find when relative extrema occur.

Accepted Answer

There is a relative

Question 19

Let y =   
(a)Determine all x - and y-intercepts.
(b)Determine equations of all vertical asymptotes 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)(-2,0)
(b)y = 0,x = 0
(c)y' = - @#IMG-DLM&_TB65

Question 20

Use the second derivative test to find the relative extremas of f(x)= 4   
- 6x and where they occur.If the relative extremas can not be determined by the second derivative test,state so.

Accepted Answer

Relative Maximum = f @#IMG-DLM&_TB6578_1

The function f(x)= - 6x + 8 is decreasing on

Find the absolute extrema for y = + - 3x + 7 on the interval and where they occur.

If f(x)= + 2 - 4x + 10,then f is

Find all the critical values of f(x)= - 2 .

The demand equation for a monopolist's product is p = 2700 - ,where p is the price per unit (in dollars)when q units are demanded. (a)Find the value of q for which revenue is maximum. (b)What is the maximum revenue?

If f(x)= - 6 + 3,then f has an inflection point when x =

A rectangular plot of ground is to be fenced in so that it has an area of 15,000 square feet.The plot is to be divided in half with a fence parallel to one pair of sides.Find the dimensions of the plot if the least amount of fencing is to be used.

If y = + 4 - 3x + 4,use the second-derivative test to find all values of x for which (a)relative maxima occur (b)relative minima occur.

The revenue equation for a company is given by R(x)= 68.04x - 0.07 .Determine when relative extrema occur on the interval (0,∞).

Sensitivity to a drug depends on the dosage size x according to the equation s = 100x - .Find the dosage that maximizes sensitivity.

An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.

Find all the critical values of f(x)= - 8 + 3.

The graph of a function is given.Find (a)the open intervals on which the function is increasing or decreasing; (b)the coordinates of all relative extrema.

Find two numbers whose sum is 50 and such that the product of one of them and five more than the other is a maximum.

On the interval ,the function y = + 3 - 9x + 27 has an absolute maximum when x =

The profit equation for a taco stand is given by P(x)= -0.4 + 100x - 100,where x is the number of tacos sold,and P(x)is the profit in dollars.Use the first-derivative test to find when relative extrema occur.

The cost equation for a cookie store is given by C(x)= - 6 + 250,where x is the number of cookies made (in dozens)and C(x)is the cost in dollars.Use the first-derivative test to find when relative extrema occur.

Use the second derivative test to find the relative extremas of f(x)= 4 - 6x and where they occur.If the relative extremas can not be determined by the second derivative test,state so.

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

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Exam 14: Curve Sketching

The function f(x)= - 6x + 8 is decreasing on

Find the absolute extrema for y = + - 3x + 7 on the interval and where they occur.

If f(x)= + 2 - 4x + 10,then f is

Find all the critical values of f(x)= - 2 .

The demand equation for a monopolist's product is p = 2700 - ,where p is the price per unit (in dollars)when q units are demanded. (a)Find the value of q for which revenue is maximum. (b)What is the maximum revenue?

If f(x)= - 6 + 3,then f has an inflection point when x =

A rectangular plot of ground is to be fenced in so that it has an area of 15,000 square feet.The plot is to be divided in half with a fence parallel to one pair of sides.Find the dimensions of the plot if the least amount of fencing is to be used.

If y = + 4 - 3x + 4,use the second-derivative test to find all values of x for which (a)relative maxima occur (b)relative minima occur.

The revenue equation for a company is given by R(x)= 68.04x - 0.07 .Determine when relative extrema occur on the interval (0,∞).

Sensitivity to a drug depends on the dosage size x according to the equation s = 100x - .Find the dosage that maximizes sensitivity.

An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.

Find all the critical values of f(x)= - 8 + 3.

The graph of a function is given.Find (a)the open intervals on which the function is increasing or decreasing; (b)the coordinates of all relative extrema.

Find two numbers whose sum is 50 and such that the product of one of them and five more than the other is a maximum.

On the interval ,the function y = + 3 - 9x + 27 has an absolute maximum when x =

The profit equation for a taco stand is given by P(x)= -0.4 + 100x - 100,where x is the number of tacos sold,and P(x)is the profit in dollars.Use the first-derivative test to find when relative extrema occur.

The cost equation for a cookie store is given by C(x)= - 6 + 250,where x is the number of cookies made (in dozens)and C(x)is the cost in dollars.Use the first-derivative test to find when relative extrema occur.

Use the second derivative test to find the relative extremas of f(x)= 4 - 6x and where they occur.If the relative extremas can not be determined by the second derivative test,state so.

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