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?

Answer 1

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).....

Answer 2

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

Answer 3

okay thanks

Answer 4

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

Answer 5

show me

Answer 6

please