Trig Function Derivation Question

[waealu]

Homework Statement

I am working on some calculus homework and I am stumped by this question. It is in the section "derivatives of trigonometric functions." It seems like it should be easy, but I can't think of where to start. I don't need any answers and you don't need to present any calculations, I only need an idea of where to start. Thank you.

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?

Homework Equations

I determined the derivative of the curve to be: 1/(x+1)^2

The Attempt at a Solution

I began by finding the derivative (as stated above), but I'm not sure where to go next. Thanks.

 

[Tedjn]

Let f(x) = x/(x+1). The derivative at x gives you the slope of the tangent line at x. This tangent line passes through the point (x,f(x)), which is enough information to give you the equation of the line. You need to find out when, if ever, it passes through (1,2) as well.

 

[waealu]

Okay. I've got it. Thanks!