How do you find the average rate of change for the function #f(x)= x^3 +2x^2 + x# on the indicated intervals [-1,2]?

1 Answer
Aug 13, 2015

The average rate of change is #6# (#f# units per #x# unit)

Explanation:

The rate of change is the ratio of the change of one quantity divided by the change of another.

Average rate of change of a function #f(x)# (with respect to #x#) is the change in #f(x)# divided by the change in #x#, so

Average rate of change of a function #f(x)# on an interval #[a,b]# is:

#(f(b)-f(a))/(b-a)#.

In this question: the function is #f(x) = x^3+2x^2+x# and the interval is #[a,b] = [-1,2]#

So the average rate of change of #f# on the interval is:

#(f(2)-f(-1))/(2-(-1)) = (18-0)/(2+1) = 18/3 = 6#.

If we had units for #x# and #f(x)# we would use them as #f# units per #x# unit