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Math Help - horizontal tangent

  1. #1
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    Thumbs down horizontal tangent

    For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.)
    f (x) = 2x^3 + 6x^2 + 2 x + 9

    horizontal tangent has a zero slope
    so would i differentiate it before i set the equation =0?
    Last edited by mr fantastic; September 27th 2009 at 03:18 AM.
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  2. #2
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    yes, Differentiate first.
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  3. #3
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    well i got 6x^2+12x+2, do i set this equal to 0 or what next? i've been studying math all day long. i'm f'serious. >.<,
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  4. #4
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    Yep set it to zero.
    it becomes

     6x^2 + 12x + 2 = 0

     2(3x^2 + 6x + 1) = 0

     3x^2 + 6x + 1 = 0

    and then find the values of x, using the quadratic formula or completing the square.

    the answer becomes

     x = \frac{-6 \pm \sqrt{6^2 - 12}}{6}

     = \frac{-6\pm \sqrt{24}}{6}

     = -0.1835\ or\ -1.8165
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