Question 1

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places.
The maximum profit is $__________
What would be the price/bottle in this case? Round the answer to the nearest cent.
$__________/bottle

Accepted Answer

;

Question 2

Find the horizontal and vertical asymptotes of the graph of the function.

Accepted Answer

A)   Vertical asymptote: x = -4
B)   Vertical asymptotes: x = -4, x = -1 and x = 0
C)   Vertical asymptotes: x = -4 and x = -1; Horizontal asymptotes: y = 1 and y = -1
D)   Vertical asymptote: x = -4; Horizontal asymptotes: y = 0 A

Question 3

Answer true or false.
If f is defined on a closed interval  , then f has an absolute maximum value.

Accepted Answer

The answer of Answer true or false.
If f is defined...

Question 4

You are given the graph of a function f. Determine the intervals where f is concave downward.

Accepted Answer

A)   
B)   
C)   
D)

Question 5

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb. The estimated demand for the cookies is 1,000,000 1-lb containers. The setup cost for each production run is $250, and the manufacturing cost is $.30 for each container of cookies. The cost of storing each container of cookies over the year is $.20. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost?
Hint: Show that the total production cost is given by the function  .
Then minimize the function  on the interval (0, 1,000,000).

Accepted Answer

A)   50,000
B)   40,000
C)   45,000
D)   35,000

Question 6

The average speed of a vehicle on a stretch of a route between 6
A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________
A.M.
average speed = __________ mph
A.M. and 10
A.M. on a typical weekday is approximated by the function
  , where f (t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6

Accepted Answer

The answer of The average speed of a vehicle on...

Question 7

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by  . When is the concentration of the drug increasing, and when is it decreasing?

Accepted Answer

A)   Increasing on  , decreasing on
B)   Increasing on  , decreasing on
C)   Increasing on  , decreasing on
D)   Increasing on  , decreasing on
E)   Increasing on  , decreasing on

Question 8

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A)   No relative maximum; Relative minima 
B)   No relative maximum or minimum
C)   Relative maximum:  ; No relative minimum
D)   Relative minimum:  ; No relative maximum
E)   Relative maximum:  ; Relative minima

Question 9

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Accepted Answer

A)   Absolute maximum value:  ; absolute minimum value:
B)   Absolute maximum value:  ; absolute minimum value:
C)   Absolute maximum value:  ; absolute minimum value:
D)   No absolute extrema

Question 10

Find the inflection points of the following function.

Accepted Answer

A)    and
B)    , , and
C)    and
D)    and
E)    and

Question 11

Show that the function  has no relative extrema on  .

Accepted Answer

A)   The function has no relative extrema by definition of the derivation.
B)   The derivation of the function  is . At every point the derivative exists and does not equal to 0. So by definition the function has no relative extrema on this interval.
C)   The function has no relative extrema because  does not equal to 0 at any point.

Question 12

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A)   Relative maximum: g(0)  = - 9; No relative minima
B)   No relative maxima; Relative minima g(0)  = - 9
C)   Relative maximum: g(9)  = 0; Relative minimum f(0)  = - 9
D)   No relative maxima or minima

Question 13

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A)   No relative maximum; Relative minimum f(2)  = - 4
B)   Relative maximum: f(2)  = 4; Relative minimum f(0)  = - 2
C)   Relative maximum: f(2)  = - 4; No relative minimum
D)   No relative maxima or minima.

Question 14

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Accepted Answer

A)   Absolute maximum value:  ; absolute minimum value: none
B)   Absolute maximum value: none; absolute minimum value: 0
C)   Absolute maximum value: none; absolute minimum value: 
D)   No absolute extrema

Question 15

The height (in feet) attained by a rocket t sec into flight is given by the function  .
When is the rocket rising and when is it descending?

Accepted Answer

The answer of The height (in feet) attained by a...

Question 16

Find the inflection points, if any, of the following function. Otherwise, answer no solution.

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 17

The owner of the Rancho Los Feliz has 2,600 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Sketch the graph of the function having the given properties.  ,  ,  ,  ,  on  ,  on  , inflection point at

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the inflection points, if any, of the function. Otherwise, answer no solution.

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 20

The owner of the Rancho Los Feliz has 3,000 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose?  What is this area?
__________

Accepted Answer

The answer of The owner of the Rancho Los Feliz...

Exam 4: Applications of the Derivative

Find the horizontal and vertical asymptotes of the graph of the function.

Answer true or false. If f is defined on a closed interval , then f has an absolute maximum value.

You are given the graph of a function f. Determine the intervals where f is concave downward.

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by . When is the concentration of the drug increasing, and when is it decreasing?

Find the relative maxima and relative minima, if any, of the function.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the inflection points of the following function.

Show that the function has no relative extrema on .

Find the relative maxima and relative minima, if any, of the function.

Find the relative maxima and relative minima, if any, of the function.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

The height (in feet) attained by a rocket t sec into flight is given by the function . When is the rocket rising and when is it descending?

Find the inflection points, if any, of the following function. Otherwise, answer no solution.

The owner of the Rancho Los Feliz has 2,600 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Sketch the graph of the function having the given properties. , , , , on , on , inflection point at

Find the inflection points, if any, of the function. Otherwise, answer no solution.