Find all the points (x,y) on the graph of y=x/(x-1) with tangent lines perpendicular to the line y=x+2

Question

mathmale · Answer

What course are you in?  This is a very interesting problem!
First, do you know how to obtain an expression (function) for the slope of f(x) = x / (x-1)?  If so, please do so.

Slope of tangent line to the graph of x / (x-1) at any x other than 1 is ... ?

anonymous · Answer

I'm taking up CE :)

anonymous · Answer

Sorry haven't been in schl quite some time so really have no idea

mathmale · Answer

CE = ???

I'd suggest you graph f(x) = x / (x-1) as best you can, as it will tell you a lot about the solution to this math problem.

Also, if you know how to find the derivative of a rational function, please find the derivative of f(x).  This derivative represents the slope of the tangent line to the curve at any x other than x = 1.

anonymous · Answer

civil engr

mathmale · Answer

Cool.  I'm an electrical engineer.  I'm assuming you're taking calculus.  Mind applying the quotient rule to y = x/(x-1) to determine the derivative (dy/dx), and thus determine the slope of the tangent line to the graph at any x (other than x=1)?