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Thread: Derivative

  1. #1
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    Derivative

    find the equation of the tangent line to $\displaystyle f(x) = x+\sqrt{x}$ at (4,6)


    $\displaystyle \frac{(x+\sqrt{x})-(4+\sqrt{4})}{x-4}$

    = $\displaystyle \frac{x-4+\sqrt{x}-\sqrt{4}}{x-4}$

    why am I havin so much trouble getting that denominator out of there
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  2. #2
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    $\displaystyle \frac{(x + \sqrt{x}) - (4 + \sqrt{4})}{x-4} =$

    $\displaystyle \frac{x + \sqrt{x} - 6}{x-4} =$

    $\displaystyle \frac{(\sqrt{x} + 3)(\sqrt{x} - 2)}{(\sqrt{x} + 2)(\sqrt{x} - 2)} =$

    $\displaystyle \frac{\sqrt{x} + 3}{\sqrt{x} + 2}$

    now take the limit
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