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Math Help - Very Hard Tangent Line Question

  1. #1
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    Very Hard Tangent Line Question

    The green line represents f(x) = (x^2)*sqrt(3) - 1 and red one represents a line which you only know the slope of which is sqrt(3). And for the purpose of my question you can ignore the values in the plot. And my question is how do you compute A (the point at which the red line intercests do green one) knowing that the red line is tangent to the green line at A, without using a derivative?
    And without using math more advanced than 11th grade geometry.
    And here is the plot:
    http://i134.photobucket.com/albums/q...nsilv/plot.jpg
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  2. #2
    MHF Contributor
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    HI

    First of all I would like to warn you on the fact that I do not know what is 11th grade therefore maybe my answer will not be satisfying

    The green curve represents f(x) = \sqrt{3}\:x^2 - 1
    The red line represents g(x) = \sqrt{3}\:x + p

    They cross at a point defined by
    \sqrt{3}\:x^2 - 1 = \sqrt{3}\:x + p

    \sqrt{3}\:x^2 - \sqrt{3}\:x - 1 - p = 0

    The red line being tangent to the green curve this equation has only one solution which is x=1/2 (found by completing the square for instance)
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