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anonymous

  • 5 years ago

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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  1. anonymous
    • 5 years ago
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    I have the 1st derivative as (-4x^3+105x^2-70x+1225) / (x^2+35)^2 is this correct?

  2. amistre64
    • 5 years ago
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    \[(x^2 +35)(35-2x) - (2x)(35x-x^2) // (x^2+35)^2\] the "//" means "all over" (x^2+35)^2

  3. amistre64
    • 5 years ago
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    -70x/(x^2+35)^2 is what I get...and im prone to error ;)

  4. amistre64
    • 5 years ago
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    and I see an error....

  5. amistre64
    • 5 years ago
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    \[35x^2 +35^2 -2x^3 -70x -70x^2 +2x^3\]

  6. amistre64
    • 5 years ago
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    \[-35x^2 -70x +35^2\]

  7. amistre64
    • 5 years ago
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    -35(x^2 +2x -35)//(x^2-35)^2

  8. amistre64
    • 5 years ago
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    thats correct :)

  9. amistre64
    • 5 years ago
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    now when (x^2 +2x -35) is equal to zero, youll have your answer I beleive

  10. amistre64
    • 5 years ago
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    (x+7)(x-5) x = -7 or x=5 take your pick ;)

  11. anonymous
    • 5 years ago
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    ok I got lost back at the begining. After the quotient rule when I multiply I get \[-2x ^{3 } + 35x ^{2} - 70x +1225 - 70x ^{2} +2x ^{3} // (x ^{2} + 35)^{2}\]

  12. anonymous
    • 5 years ago
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    never mind I see where we have the same. you just wrote it a little differently. the 35^2 instead of 1225.

  13. amistre64
    • 5 years ago
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    yeah... I figured it be easier on me to not figure 35^2 out ...

  14. amistre64
    • 5 years ago
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    925+150+150 = 925+300 = 1225

  15. amistre64
    • 5 years ago
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    thats my georgia math :)

  16. anonymous
    • 5 years ago
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    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

  17. amistre64
    • 5 years ago
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    factor out the negative so you have a "normal" quadratic to play with..

  18. amistre64
    • 5 years ago
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    same results, just easier to get to

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