A manufacturer sells video games with the following cost and revenue functions (in dollars) where x is the number of games sold, for 0 less than or equal to x less than or equal to 3300.

C(x)= 0.32x^2-0.00004x^3
R(x)= 0.848x^2-0.0002x^3

Determine the intervals on which the profit function is increasing.

Therefore the profit interval is (0,2200).

Step-by-step explanation:

Given cost and revenue function are respectively,

and

where x is the number of game sold, .

Therefore the profit function is

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

To determine the profit interval where profit function increasing, we have to find the critical point of P(x). We set the first order derivative equal to 0.

Therefore,

⇒x(1.056-0.00048 x) =0

   or,    

Now choose two point one is less than 2200 and other is greater than of 2200.

We choose x= 1000 and x= 2000

Now

 >0

<0

Therefore the profit interval is (0,2200).