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.
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.
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 $\displaystyle (0,4)$.