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Average rate of change

The average rate of change tells how much a function changes per unit on average over an interval. Graphically it is the slope of the line through two points on the graph, called a secant.

\frac{\Delta y}{\Delta x} = \frac{f(b) - f(a)}{b - a}

average rate of change from a to b

Symbols

$\Delta y$	change in function value
$\Delta x$	change in x

Example

$f(x) = x^2$ from $x = 1$ to $x = 3$ :

$\frac{9 - 1}{3 - 1} = 4$ .

A rate of change has units: for example metres per second or dollars per year.

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