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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?

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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

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OpenStudy (anonymous):

please

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