Calculus homework?
BUS 305
Calculus Unit Assignment 2
Description: Problems dealing with derivatives and other basic concepts and their application to business scenarios.
General Instructions: Because of the notation involved, the questions for this assessment are in this Word document. Work out your answers on paper and choose the letter of the best answer, then go to the Assignments folder in Blackboard and mark the correct answer for each question.
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 -2 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 5 weeks?
a. Receipts are 10240*6 = 61440
b. Receipts are growing at a rate of 9620.6 per week
c. Receipts are shrinking by a rate of 925 per week
d. Receipts are shrinking by a rate of 1547.24 per week
Use this situation for questions 3 and 4.
The cost to produce x units of a product is given by the formula
3. What is the cost of producing 10 units?
a. 150
b. 9700
c. 90
d. 8500
4. When we are already producing 10 units, what do we estimate (using the derivative) as the cost of the 11th unit?
a. 84
b. 87
c. 90
d. 210
5. At what value of x does this function reach a critical point, and what is it?
a. x = 0.4, maximum
b. x = 0.4, minimum
c. x = 0.4, point of inflection
d. there is no real value of x that causes the function to reach a critical point
6. The selling price of a product is $360, 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?
a. x = 3
b. x = 4
c. x = 30
d. x = 100
7. Find the derivative of this function
a. 
b. 
c. 
d. 
8. Find the derivative of this function.
a. 
b. 
c. 
d. 
9. Find the derivative of this function
a. 
b. 
c. 
d. 
10. Consider the revenue function 
. How fast is revenue changing at year 5?
a. -8
b. 38
c. 140
d. 210
Use this information for questions 11 – 15.
A function has the following characteristics:
The function has three critical points
When x = 30, the first derivative is negative
When x = 20, the first derivative is zero
When x = 50, the first derivative is zero and the second derivative is positive
When x = 80, the first derivative is zero
Indicate whether each of these statements is true or false. It may be helpful to create a rough sketch of the function prior to answering the questions.
11. T F When x = 40, the first derivative is positive
12. T F When x = 20 the second derivative is positive
13. T F When x = 12 the first derivative is positive
14. T F The basic shape of this curve is more like an M than a W
15. T F For any value of x between 50 and 80, the first derivative will always be negative
