Thread: Find intersect point of tangent line to a graph

The tangent line to the graph of y=x+ (2/x) at the point (1,3) intersects the y-axis where?

I'm not sure where to start...

take a derivative of y with respect to x. This represents the slope of a line tangent to the graph at a given point. It gives you the point (1,3) so plug in x = 1 in dy/dx this gives you the slope of the tangent line. You know a point that the line passes through, and you know its slope, so you can get the equation of the line with y = mx + b, and of course whatever b turns out to be is your answer.

(i got b = 4)

to show my work for anyone who happens upon this:

d/dx = 1-(2/x^2). plugging in 1 (from the point) gives me -1.

y-y1=m(x-x1), so i get y = -x +4

4 =b


thanks!