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Asymptotes math problem

  1. Jun 6, 2010 #1
    1. The problem statement, all variables and given/known data

    f(x) = 1/(x+1)

    If tangents to curve at x=x1 and x=x2 are parrallel and if x1 is not equal to x2
    show that x1 + x2 = -2

    3. The attempt at a solution

    Well i found my equations for the asymptotes
    Horizontal: x=0
    Vertical: x= -1

    and then i would say that if they were parrallel that the slopes are equal and therefore at the point x1 and the point x2 the slopes are equal

    f1(x) = -1/(x+1)2

    If i sub in x1 and x2, they will be equal and the question says they arent?

    Can anyone help me please?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jun 6, 2010 #2


    Staff: Mentor

    Re: Asymptotes

    Your title is misleading - this problem doesn't have anything to do with asymptotes of either kind.

    You are give that the tangent lines are parallel at x = x1 and x = x2, so f'(x1) = f'(x2). This means that -1/(x1 + 1)2 = -1/(x2 + 1)2. Solve that equation, keeping in mind that x1 [itex]\neq[/itex] x2, and that if a2 = b2 ==> a = b or a = -b.
  4. Jun 6, 2010 #3
    Re: Asymptotes

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