# Math Help - differentiation tangent lines question

1. ## differentiation tangent lines question

How many tangent lines to the curve y=x/(x+1) pass through the point (1,2)? At which points do these tangent lines touch the curve?

2. Hi
Originally Posted by cityismine
How many tangent lines to the curve y=x/(x+1) pass through the point (1,2)? At which points do these tangent lines touch the curve?
Let $f(x)=\frac{x}{x+1}$

The equation of the tangent line to the curve of $f$ at $a$ is $y=f(a)+(x-a)f'(a)$. As you're looking for the tangent lines which pass through $(1,2)$, you've to find the solutions of $2=f(a)+(1-a)f'(a)$. Can you take it from here ?

3. I took it from exactly where you left it. The answer I got matches the one in the book, so I know it's right.