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Finding a line passing through a known point/tangent to a curve at an unknown point

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the line passing through the point (0,-18) and tangent to the curve y=x^3-2 at some point.


    2. Relevant equations
    y=mx+b


    3. The attempt at a solution
    Well, I know the derivative is 3x^2, and that should be the slope of the line at the point of tangency. I'm just not sure how to find out what point the curve shares with the line! I know that seems like a pretty bad attempt at a solution, I just need a hint about where to start with this one.
     
  2. jcsd
  3. Oct 16, 2011 #2

    SammyS

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    Re: Finding a line passing through a known point/tangent to a curve at an unknown poi

    The line you want passes passes through a point on the curve y = x3 - 2 , so, as an ordered pair, this point is (x, x3 - 2). The slope of the line is given as
    m = 3x2, for the same value of x that's in the ordered pair.

    Now, we could use the point - slope form of a line, but the point given to us is the y intercept for any line passing through it. Use the slope-intercept form of a line. y = mx + b, where b = -18.

    (x3 - 2) = (3x2)(x) - 18 .

    Solve this equation for x, to find the x value for a point on the parabola.
     
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