The retaionship between a magnitude of a funtion and it's rate of change is fairly straightforward. a functions rate of change is simply its derivative. Let's do a few examples.



To find the rate of change of this function, simply find its derivative (as stated above).



Notice the rate of change of this function is constant. Lets do a slightly more complex example.




Notice how with each increased unit for x, the rate of changed is doubled. Lets expand this concept a little farther.



For this function, the rate of change increases even faster with each progressive x value. As a rule, the higher the magnitude of a function, the greater the rate of change for that function. It really is that simple!

source: Calculus with Analytic Geometry: Eighth Edition. Houghton Mifflin Company, Boston. pages 96-114 (first example taken from page 98)