What does average rate of change mean?

1 Answer
Gió
Jul 31, 2015

The average rate of change of a function y=f(x), for example, tells you of how much the value of the function changes when x changes.

Explanation:

Consider the following diagram:
enter image source here
when x changes from x1 to x2 the value of the function changes from y1 to y2. The average rate of change will be:
(y2-y1)/(x2-x1) and it is, basically the slope of the blue line.

For example:
if x1=1 and x2=5
and:
y1=2 and y2=10
you get that:
Average rate of change=(10-2)/(5-1)=8/4=2

This means that for your function: color(red)("every time "x" increases of 1 then "y" increases of 2"
Obviously your function is not a perfect straight line and it will change differently inside that interval but the average rate can only evaluate the change between the two given points not at each individual point.

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