A manufacturer sells video games with the following cost and revenue functions (

Question

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) = 0.19x^2 - 0.00004x^3 R(x) = 1.054x^2 - 0.0002x^3 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.

Explanation / Answer

profit P(x)=revenue R(x) -cost C(x)

P(x)=(1.054x2-0.0002x3)-(0.19x2-0.00004x3)

P(x)=(0.864x2-0.00016x3)

differentiate with respect to x

P'(x)=(0.864*2x-0.00016*3x2)

P'(x)=(1.728x-0.00048x2)

profit function is increasing when P'(x) >0

(1.728x-0.00048x2)>0

(0.00048x2-1.728x)<0

x(0.00048x -1.728)<0

x>0 ,x<1.728/0.00048

x>0, x<3600

interval of increase is (0,3600)

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