1. The derivative of a function is given byHow does the original function behave at x = 2? The...

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1. The derivative of a function is given by How does the original function behave at x = 2? The original function is increasing at x = 2. The original function is decreasing at x = 2. The original...

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1. The derivative of a function is given by

How does the original function behave at x = 2?

The original function is increasing at x = 2.
The original function is decreasing at x = 2.
The original function has reached a relative maximum at x = 2.
The original function is equal to 54 when x = 2.

2. The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the movie has been playing.

What is the rate of change of weekly receipts per theater after 10 weeks?

Receipts are 5207.8
Receipts are growing at XXXXXXXXXXper week
Receipts are shrinking by XXXXXXXXXXper week
Receipts are shrinking by 527 per week

3. The cost to produce x units of a product is given by the formula

What is the cost of producing 8 units?

277
312
35
51

4. When we are already producing 8 units, what do we estimate as the cost of the 9^th unit?

363
34
38
51

5. At what value of x does this function reach a critical point, and what is it?

X = 2.5, maximum
X= 2.5, minimum
X = 2.5, point of inflection
There is no real value of x that causes the function to reach a critical point

6. The selling price of a product is $400, and the manufacturer is able to sell every unit it makes. The cost of producing x units is given by this formula:

How many units should be produced in order to maximize profit?

X=25
X=4
X=100
X=1000

7. The marginal revenue is given by the expression

If the revenue when x=10 is known to be 1000, give the functional representation of revenue.

6
0

005_lblgjk-ejlm4zvk.docx

Answered Same Day Dec 21, 2021

David · Accepted Answer

1.  The derivative of a function is given by 
  ( )                
  
How does the original function behave at x = 2? 
a. The original function is increasing at x = 2. 
b. The original function is decreasing at x = 2. 
c. The original function has reached a relative maximum at x = 2. 
d. The original function is equal to 54 when x = 2.
Original function = f(x) = ∫  ( )   = ∫                 
 
= 
   
 

 

 

=    -   3       
 
For x = 2, f(x) =  ( ) -( )  3( )    ( ) = 32-8+12-20 = 16 
For x  2, say x = 2.1, f(x) =  (   ) -(   )  3(   )    (   )        
 
Thus for x  2, f(x) > f(2). 
Hence original function is increasing at x = 2
Answer: a 
 
2. The function below approximates the weekly box office receipts for a popular movie, where x = the number of weeks the 
movie has been playing. 
 ( )                             
What is the rate of change of weekly receipts per theater after 10 weeks?

1. The derivative of a function is given by How does the original function behave at x = 2? The original function is increasing at x = 2. The original function is decreasing at x = 2. The original...

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