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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?

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The average rate of change is defined over some finite interval $\Delta x$ to be

$$ \frac{\Delta y}{\Delta x} $$

The rate of change is the rate at which the function changes at one particular point and is found by taking the limit

$$ \lim_{\Delta x\to 0} \frac{\Delta y}{\Delta x} $$

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 $m$).

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