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Average rate of change

The average rate of change tells how much a function changes per unit of $x$ over an interval. It is the slope of the secant, the straight line through two points on the graph. When the interval becomes very small, it approaches the instantaneous rate of change, the derivative.

\frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

average rate of change

Symbols

$\Delta y$	change in function value
$\Delta x$	length of the interval

Example

$f(x) = x^2$ from $x = 1$ to $x = 3$ : $\frac{9 - 1}{3 - 1} = 4$ .

Remember the unit, for example metres per second or kroner per year.

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Part of Mathematics 1T: Differentiation and rate of change.