Average Rate of Change

Average Rate of Change
ARC

The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph.

Any of the following formulas can be used.

ARC = average rate of change = \(\frac{{\Delta y}}{{\Delta x}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{f\left( {{x_2}} \right) - f\left( {{x_1}} \right)}}{{{x_2} - {x_1}}} = \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\)

Note: This is the same thing as the slope of the secant line of a curve.

 

 

See also

Instantaneous rate of change, mean value theorem