Mathematics
OpenStudy (anonymous):

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?

OpenStudy (anonymous):

I know I at least have to find the slope of the tangent line first off, i.e., the derivative of the curve (y), but uh is it 1/(x+1)^2 or is it -x/(x+1).....

OpenStudy (anonymous):

derivative is $\frac{1}{(x+1)^2}$ so if the line is tangent it must satisfy two equation

OpenStudy (anonymous):

okay thanks

OpenStudy (anonymous):

if you have a point on the curve it looks like $(x, \frac{x}{x+1})$ and the slope of the line must be the derivative, so your job is to solve $\frac{\frac{x}{x+1}-2}{x-1}=\frac{1}{(x+1)^2}$ for x

OpenStudy (anonymous):

show me

OpenStudy (anonymous):