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Thread: simple problem need someone to do it so i can compare answers

  1. #1
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    simple problem need someone to do it so i can compare answers

    The tangent at (2,2) to the curve y=x/(x-1) meets the axis at M. find the coordinates of M?

    does anyone know the answer please tell me.
    Last edited by mr fantastic; Oct 2nd 2009 at 09:41 PM. Reason: Tidied up the post
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by kayla220220 View Post
    <H1 class=subject>The tangent at (2,2) to the curve y=x/(x-1) meets the axis at M. find the coordinates of M?

    does any1 noee the answer pleaseee tell meeee
    </H1>
    The derivative of $\displaystyle x(x-1)^{-1}$ is $\displaystyle -x(x-1)^{-2}+(x-1)^{-1}$

    Evaluating this at $\displaystyle x=2$ gives $\displaystyle y'=-1$

    Using $\displaystyle (x,y)=(2,2)$ and $\displaystyle m=-1$, we have:

    $\displaystyle 2=-1\cdot 2+b \implies b=4$

    So the equation of the tangent line is $\displaystyle y=-x+4$.

    This intersects the x-axis at $\displaystyle (4,0)$ and the y-axis at $\displaystyle (0,4)$.
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