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