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.

- Oct 2nd 2009, 08:12 PMkayla220220simple 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. - Oct 2nd 2009, 08:35 PMredsoxfan325
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 $\displaystyle (0,4)$.