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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