Doug C. answered • 12/07/21

Math Tutor with Reputation to make difficult concepts understandable

Every point on the graph of y will be of the form (x, x/(x+2)). The slope of a line passing through a point with those coordinates and the point (1,2) will look like this:

m = ( 2 - x/(x+2) ) / (1-x)

The derivative of y (dy/dx) is y' = 2/(x+2)^{2}. That is also a formula for the slope of a line with an x coordinate of x.

So these two expressions must be equal:

(2 - x/(x+2) ) / ( 1 - x) = 2/(x+2)^{2}.

Here you probably want to cross multiply, ending with a quadratic equation which you can solve for x using the quadratic formula--giving the required to values for x.

Try the above and check it out here:

desmos.com/calculator/n8utwh9qbm