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Tangent lines

  1. May 4, 2008 #1
    Can someone help me with this problem?

    Consider the curve defined by y=x/(x+1). (1,2) is a point NOT on the curve.
    Find the equations of the two tangent lines to the curve passing through the point
  2. jcsd
  3. May 4, 2008 #2


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    Gold Member

    There are some ways to attack this problem but my first instinct is to sketch or print the graph then mark the point (1,2) then take a ruler and carefully draw the tangent lines touching one point on each side of the graph. Then take the derivative around those points and use the formula of a line (y=mx+c) and check to see if the gradients run through the points.

    This is perhaps tedious to say the least but I don't know how else to tackle the problem without any more information.

    btw winplot should help with this.
  4. May 4, 2008 #3


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    Homework Helper

    hihi davedave! :smile:

    Write y = ax + b for a typical line.

    What is the restriction on a and b for it to pass through (1,2)?

    Now find the equation for the points of intersection of that line with y=x/(x+1).

    That should be a quadratic equation.

    What is the condition for that equation to have two equal roots? :smile:
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