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Tangent Line

  1. Oct 2, 2007 #1
    [SOLVED] Tangent Line

    1. The problem statement, all variables and given/known data
    Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3)

    2. Relevant equations

    3. The attempt at a solution

    At first I thought I knew how to do this problem, I found the derivative of the equation got:

    y' = 2x ; then I plugged in x=2 to find the slope of the tangent however then i realized this is not the correct point to plug in because this is not the point that the line is actually going to be hitting the original graph at; I don't know how you would find this said point to plug in for x to get the slope can anyone steer me in the right direction
  2. jcsd
  3. Oct 2, 2007 #2


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    You are looking for a line. You have the slope, and a point that the line goes through. That's sufficient information to derive the line equation.
  4. Oct 2, 2007 #3
    I don't have the slope though because I don't know what point the line is tangent to on the curve so how can i plug a value into the derivative to get slope
  5. Oct 2, 2007 #4


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    y' = 2x is the family of all lines that are tangent to x^2. You are supposed to find the one that goes through (2,3).
  6. Oct 2, 2007 #5
    oh i see thank you for your help :)
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