1. The derivative of a function is given by
f'(x)= 8x3 - 3x2 + 6x - 10
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.
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.
f(x)= 10369-863x+16.8x2+17888x-1
What is the rate of change of weekly receipts per theater after 10 weeks?
a. Receipts are 5207.8
b. Receipts are growing at 5207.8 per week
c. Receipts are shrinking by 705.88 per week
d. Receipts are shrinking by 527 per week
3. The cost to produce x units of a product is given by the formula
C(x)= 200-10x+3x2
What is the cost of producing 8 units?
a. 277
b. 312
c. 35
d. 51
4. When we are already producing 8 units, what do we estimate as the cost of the 9th unit?
a. 363
b. 34
c. 38
d. 51
5. At what value of x does this function reach a critical point, and what is it?
f(x)= 7x2 - 35x + 400
a. X = 2.5, maximum
b. X= 2.5, minimum
c. X = 2.5, point of inflection
d. There is no real value of x that causes the function to reach a critical point.