A manufacturer sells video games with the following cost and

A manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold. Determine the interval(s) on which the profit function is increasing. C(x) = 0.13x2-0.00014x3 R(x) = 0.436x2-0.0002x3 Select the correct choice below and fill in any answer boxes within your choice. The profit function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) The profit function is never increasing.

Solution

Profit = revenue - cost

P(x) = R(x) - C(x)

= 0.306x² - 0.00006x³

P \' (x) = 0.612x - 0.00018x²

= x(0.612 - 0.00018x)

= - 0.00018 x(x - 3400)

For profit increasing, P \'(x) > 0

-0.00018 x(x - 3400) > 0

x(x - 3400) < 0

x (0, 3400)

Therefore, the profit increase on the interval (0 , 3400)