The revenue derived from the production of x units of a particular commodity is: R(x)= (35x-x^2)/(x^2+35) million dollars. What level of production results in maximum revenue? What is the maximum revenue?

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The revenue derived from the production of x units of a particular commodity is: R(x)= (35x-x^2)/(x^2+35) million dollars. What level of production results in maximum revenue? What is the maximum revenue?

Mathematics
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I have the 1st derivative as (-4x^3+105x^2-70x+1225) / (x^2+35)^2 is this correct?
\[(x^2 +35)(35-2x) - (2x)(35x-x^2) // (x^2+35)^2\] the "//" means "all over" (x^2+35)^2
-70x/(x^2+35)^2 is what I get...and im prone to error ;)

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and I see an error....
\[35x^2 +35^2 -2x^3 -70x -70x^2 +2x^3\]
\[-35x^2 -70x +35^2\]
-35(x^2 +2x -35)//(x^2-35)^2
thats correct :)
now when (x^2 +2x -35) is equal to zero, youll have your answer I beleive
(x+7)(x-5) x = -7 or x=5 take your pick ;)
ok I got lost back at the begining. After the quotient rule when I multiply I get \[-2x ^{3 } + 35x ^{2} - 70x +1225 - 70x ^{2} +2x ^{3} // (x ^{2} + 35)^{2}\]
never mind I see where we have the same. you just wrote it a little differently. the 35^2 instead of 1225.
yeah... I figured it be easier on me to not figure 35^2 out ...
925+150+150 = 925+300 = 1225
thats my georgia math :)
ok when you factor out the 35 should it be negative. \[-35(x ^{2} + 2x - 35) // (x ^{2}+35)^{2}\] I would have put 35(-x^2-2x+35) // (x^2+35)^2 I have to start a new post. When these get too long my computer goes REALLY SLOW
factor out the negative so you have a "normal" quadratic to play with..
same results, just easier to get to

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