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?

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- Jun 5th 2008, 10:39 PMcityisminedifferentiation 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?

- Jun 5th 2008, 11:46 PMflyingsquirrel
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 ? - Jun 6th 2008, 12:38 PMcityismine
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.