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Math Help - Find values with tangent to a curve

  1. #1
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    Find values with tangent to a curve

    The question reads:

    Find the values of m for which the line y = mx - 9 is a tangent to the curve x^2 = 4y.

    All I need is the basic formula? I can't find one anywhere.
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  2. #2
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    May 2008
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    differentiate both sides
    \frac{d}{dx}(x^2)=\frac{d}{dx}(4y)

    2x=4\frac{dy}{dx}

    \frac{dy}{dx}=\frac{1}{2}x

    now \frac{dy}{dx} would be the gradient of the curve (m in the formula)

    substitute this in along with y=\frac{1}{4}x^2 (you are given this) into the equation of the line you want to find and solve this for x

    I get

    x=\pm6


    now plug these values into your expression for \frac{dy}{dx} to find the values of m (remember dy/dx=m)
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  3. #3
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    Thank you so much
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