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Math Help - [SOLVED] Isolate for x

  1. #1
    Junior Member NAPA55's Avatar
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    [SOLVED] Isolate for x

    This is some pretty freaky algebra I've got here... hopefully my derivative is right lol

    I need to set C'(x) = 0 and isolate for x (it's an optimization).

    0 = [(1000x - 200000) / (√(x2 - 400x + 44900)] + 500

    What happened to the HTML and MATH code?
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by NAPA55 and edited by Mr F View Post
    This is some pretty freaky algebra I've got here... hopefully my derivative is right lol

    I need to set C'(x) = 0 and isolate for x (it's an optimization).

     C'(x) = \frac{1000(x-200)}{\sqrt{x^2-400x+44900}}+500


     0 = \frac{1000(x-200)}{\sqrt{x^2-400x+44900}}+500
    <br />
\Rightarrow -1 = \frac{2(x-200)}{\sqrt{x^2-400x+44900}}<br />


    \Rightarrow - \sqrt{x^2-400x+44900} = 2(x-200)


    Now square both sides and solve the resulting quadratic equation.
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  3. #3
    Junior Member NAPA55's Avatar
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    Perfect, thanks!

    I subbed in my values back into my optimization problem and my answer seems correct!
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