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Math Help - Point of intersection of the tangent to the graph of y=x^2

  1. #1
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    Point of intersection of the tangent to the graph of y=x^2

    Find the coordinates of the point of intersection of the tangents to the graph of y=x^2 at the points at which it meets the line with the equation y=x+2


    Answer of this question is = (1/2, -2)


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  2. #2
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    To find A and B, set x^2 equal to x + 2 and solve for x.

    For each, use the co-ordinate pair and the slope at that point (twice the x-value?) to find the tangent-line equation.

    Then set both equations equal...
    Last edited by tom@ballooncalculus; October 1st 2009 at 01:04 AM.
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  3. #3
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    A small point: suppose x_0 and x_1 are points of intersection. Than you can find functions of tangents as:

    y = (1/f'(x_0))(x-x_0)+f(x_0)
    y = (1/f'(x_1))(x-x_1)+f(x_1)

    or

    y = (1/(2*x_0))(x-x_0)+x_0^2
    y = (1/(2*x_1))(x-x_1)+x_1^2
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