What does the limit of the derivative of a function tell you?

[aero]

Starting with the function F(x) = (x^2 - /(x+3), I took the derivative of it and got (x^2+6x+8)/(x+3)^2. Then I found the limit of that as x approached infinity, and it was 1. What does that answer tell me about F(x), the original function?

And please don't post any silly answers. Thanks.

[j_sun]

You did the derivative and the limit correctly.
In the limit, the slope of F is 1 means that eventually, the function F  is increasing 1 unit for every unit of x.
So the graph of F will eventual look like   F approximately =  1*x +b