# Rate of change vs. average rate of change of a function

What is the difference between the both? I am trying to find a separate definitions for both in a textbook, but it only defines average rate of change.

I know that average rate of change is: $$\frac { change\quad in\quad y }{ change\quad in\quad x }$$

But what is just rate of change then?

The average rate of change is defined over some finite interval $\Delta x$ to be
$$\frac{\Delta y}{\Delta x}$$
$$\lim_{\Delta x\to 0} \frac{\Delta y}{\Delta x}$$
Note that in the case of a linear function, $y=mx+c$, the rate of change and the average rate of change are identical (they both equal $m$).