How do I find the average rate of change of a function like #f(x) = 4x#?

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Sep 25, 2014

Usually we would need an interval to find the average rate of change. This is a linear function with a constant rate of change or slope so the slope and the average rate of change are the same value. Because of this reason a linear function does not need an interval.

This function is in slope intercept form, #y=mx+b#, where #m# is the slope.

#y=4x#

We see that the slope is #4#.

Just for example sake lets find the average rate of change with an interval of #x=2# to #x=5#.

Average rate of change#=(f(b)-f(a))/(b-a)#

In this example:

#f(x)=4x#
#a=2#
#b=5#

Average rate of change#=(f(5)-f(2))/(5-2)#

#=(4(5)-4(2))/(5-2)#

#=(20-8)/(3)#

#=12/3#

#=4#

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