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Derivatives Problem

  1. Oct 27, 2008 #1
    Hey everyone, I'm a new Calculus student, and this problem on derivatives is giving me lots of trouble. I can't get around it! Please help.

    1. The problem statement, all variables and given/known data

    Find the coordinates of all points on the graph of y=1-x^2 at which the tangent line passes through the point (2,0).

    2. Relevant equations

    Possibly anything related to derivatives and slope, such as:
    y-y1 = m(x-x1)
    The power rule: nx^(n-1)

    3. The attempt at a solution

    All I know is the answer is: 2 (plus or minus) squareroot(3)
    I took the derivative of the original equation in the hopes that I might see where I should be going, but I'm just stuck. I don't see where the point comes in. If someone could tell me the steps of how to get the answer so I could use that knowledge in the future, I'd really appreciate it!
  2. jcsd
  3. Oct 27, 2008 #2


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    Staff Emeritus
    Science Advisor

    Okay, the derivative of y= 1- x2 is y'= -2x and that tells you that the slope of the tangent line, at x= x0 is -2x0.

    Write the equation of the staight line, with slope -2x0 that passes through (2.0). If the coordinates of a point at which that is the tangent line are (x0,y0), then they must satisfy both that equation and y'sub]0[/sub]
    = 1- x02. That gives you two equations for x and y.
  4. Oct 27, 2008 #3
    Hang on, I think I'm on the right track:

    y-y1 = m(x-x1) --> y = 2x-4

    And then make that equal to the derived equation?

    2x-4 = 1-x^2 ?

    Which should equal

    x^2 + 2x - 5 = 0 ?

    I put that in the quadratic formula, and I'm getting an answer that's close. Am I doing the math wrong?
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