How do you find the average rate of change for the function #y= 4x²# on the indicated intervals [1,5]?

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Answer 1 · 2015-07-27T15:59:23

The average rate of change is #(Deltay)/(Deltax) = 24#

The average rate of change of function #f# on interval #[a,b]# is:

#(Deltaf)/(Deltax) = (f(b)-f(a))/(b-a)#

In this case, we have #a=1#, and #b = 5#,

and #f(x) = 4x^2#.

So we get:

#f(5) = 4(5)^2 = 100# and #f(1) = 4#, thus

#(Deltaf)/(Deltax) = (f(5)-f(1))/(5-1) = (100-4)/4 = 96/4 = 24#

Notice that the average rate of change is the same as the slope of the line connecting the points: #(1, f(1))# and #(5, f(5))#.