Question

Can someone walk me through this problem? I understand the question and the math behind it, but have no idea where to start: 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

y = x/(x+1) is given

Answer 2

what is y' ?

Answer 3

y'=1/(x+1)^2

Answer 4

Which is the slope of the curve, and the tangent line at that point

Answer 5

Any point on the curve y = x/(x+1) is of the form (x,y)

because y = x/(x+1), we can write that point as (x, x/(x+1) )

Answer 6

We have these two points

(1,2) which is given and what we want the tangent line to go through
(x, x/(x+1) )

Answer 7

Find the slope of the line through those two points to get