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Math Help - Implicit Diff Example - # 2

  1. #1
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    Implicit Diff Example - # 2

    Find the equation of the tangent line at the point (3,4)

    x^{2} + 2xy - y^{2} + x = 20

    2x + [(y)(2) + (2x)(y')] - 2yy' + 1 = 0

    2x + 2y + 2xy' - 2yy' + 1 = 0

    2x + 2y + y'[2x - 2y] + 1 = 0

     y'[2x - 2y] = -2x - 2y - 1

    y' = \dfrac{-2x - 2y - 1}{2x - 2y} - Did this come out right?

    What now? We have two variables so how to find the slope?
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    Re: Implicit Diff Example - # 2

    Hey Jason76.

    Looks very good: now just plug in the values for x and y to get the tangent gradient and recall that y - y0 = m(x - x0) for specific (x0,y0) on the line and general (x,y) on the line.
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    Re: Implicit Diff Example - # 2

    Find the equation of the tangent line at the point (3,4)

    x^{2} + 2xy - y^{2} + x = 20

    2x + [(y)(2) + (2x)(y')] - 2yy' + 1 = 0

    2x + 2y + 2xy' - 2yy' + 1 = 0

    2x + 2y + y'[2x - 2y] + 1 = 0

     y'[2x - 2y] = -2x - 2y - 1

    y' = \dfrac{-2x - 2y - 1}{2x - 2y}

    y' = \dfrac{-2(3) - 2(4) - 1}{2(3) - 2(4)}

    y' = \dfrac{-6 - 8 - 1}{6 - 8}

    y' = \dfrac{-15}{-2}

    y' = \dfrac{15}{2}

    y - 4 = \dfrac{15}{2}(x - 3)

    y - 4 = \dfrac{15}{2}x -\dfrac{45}{2} ??
    Last edited by Jason76; October 10th 2013 at 10:29 PM.
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