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Math Help - Find intersect point of tangent line to a graph

  1. #1
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    Find intersect point of tangent line to a graph

    The tangent line to the graph of y=x+ (2/x) at the point (1,3) intersects the y-axis where?

    I'm not sure where to start...
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  2. #2
    Member Mentia's Avatar
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    Bellingham, WA
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    take a derivative of y with respect to x. This represents the slope of a line tangent to the graph at a given point. It gives you the point (1,3) so plug in x = 1 in dy/dx this gives you the slope of the tangent line. You know a point that the line passes through, and you know its slope, so you can get the equation of the line with y = mx + b, and of course whatever b turns out to be is your answer.

    (i got b = 4)
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  3. #3
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    to show my work for anyone who happens upon this:

    d/dx = 1-(2/x^2). plugging in 1 (from the point) gives me -1.

    y-y1=m(x-x1), so i get y = -x +4

    4 =b


    thanks!
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