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

• October 2nd 2009, 08:12 PM
kayla220220
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?

• October 2nd 2009, 08:35 PM
redsoxfan325
Quote:

Originally Posted by kayla220220
<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?

The derivative of $x(x-1)^{-1}$ is $-x(x-1)^{-2}+(x-1)^{-1}$
Evaluating this at $x=2$ gives $y'=-1$
Using $(x,y)=(2,2)$ and $m=-1$, we have:
$2=-1\cdot 2+b \implies b=4$
So the equation of the tangent line is $y=-x+4$.
This intersects the x-axis at $(4,0)$ and the y-axis at $(0,4)$.