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Math Help - light intensity minimization

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    light intensity minimization



    My only thought on this: I have to minimize the l(x) equation it gives... But I can't figure out how to do that :S We know the power and quotient rule... no chain rule
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    Quote Originally Posted by mike_302 View Post


    My only thought on this: I have to minimize the l(x) equation it gives... But I can't figure out how to do that :S We know the power and quotient rule... no chain rule
    I = ax^{-2} + b(s-x)^{-2}

    \frac{dI}{dx} = -2ax^{-3} + 2b(s-x)^{-3}

    \frac{dI}{dx} = -\frac{2a}{x^3} + \frac{2b}{(s-x)^3}

    set the derivative equal to 0 ...

    \frac{2a}{x^3} = \frac{2b}{(s-x)^3}

    bx^3 = a(s-x)^3

    \sqrt[3]{b} \cdot x = \sqrt[3]{a} \cdot (s-x)

    x = \frac{\sqrt[3]{a} \cdot s}{\sqrt[3]{a} + \sqrt[3]{b}}<br />
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