This problem popped up in another thread and can be solved by standard methods.
For the curve y=x^2+5x
a) find the gradient of the chord PQ where P is the point (2.14) and Q is the point (2+h,(2+h)^2+5(2+h))
Let's see what geogebra can do.
1) Draw the curve by entering f(x) = x^2 + 5x.
2) Enter the point (2,14). Call it P.
3) Create a slider called h. Range it from -5 to 5.
4) Create a new point ( 2+ h, h^2 + 9h +14 ). Call it Q.
5) Draw a line between P and Q. Get the slope m of that line using the slope tool.
6) Slide h back and forth and notice the value of m in the algebra pane.
7) Record those values like this:
8) Conjecture the obvious relationship of m = h + 9.
Your geogebra worksheet should look something like this.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.