manufacturer sells video games with the following cost and revenue functions (in
ID: 2889625 • Letter: M
Question
manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold. Determine the he profit function is increasing. irborval(s) on which C(x)-0.17x -0.00006x3 Rx)-0.926x-0.0002x Select the correct choice below and fill in any answer boxes within your choioe. The profit function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) 0 A. B. The profit function is never increasing. Click to select and enter your answerfs). r of pa 97 qb max revenue (554-5*14197) 251.JPG IMG 82 078.jpg IMG 8257.JPGExplanation / Answer
C(x)=0.17x 2-0.00006x3
R(x)=0.926x2-0.0002x3
Profit,P(x)=R(x)-C(x)= 0.756x2-0.00014x3
P'(x)=1.512x-0.00042x2
Critical points ,P'(x)=0
1.512x-0.00042x2=0
x=0
1.512=0.00042x
x=3600
In (0,3600), Let's take x=3000
P'(3000)=1.512(3000)-0.00042(3000)2=756>0
And in (3600,infinity), let's take x=4000
P'(x)=1.512(4000)-0.00042(4000)2=-672<0
So the profit function is increasing in (0,3600).
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