Find the Tangent Lines of y=x/(x+1) Through (1,2)

[davedave]

Can someone help me with this problem?

Consider the curve defined by y=x/(x+1). (1,2) is a point NOT on the curve.
Find the equations of the two tangent lines to the curve passing through the point
(1,2).

 

[djeitnstine]

There are some ways to attack this problem but my first instinct is to sketch or print the graph then mark the point (1,2) then take a ruler and carefully draw the tangent lines touching one point on each side of the graph. Then take the derivative around those points and use the formula of a line (y=mx+c) and check to see if the gradients run through the points.

This is perhaps tedious to say the least but I don't know how else to tackle the problem without any more information.

btw winplot should help with this.

 

[tiny-tim]

hihi davedave!

Write y = ax + b for a typical line.

What is the restriction on a and b for it to pass through (1,2)?

Now find the equation for the points of intersection of that line with y=x/(x+1).

That should be a quadratic equation.

What is the condition for that equation to have two equal roots?