How do you find the average rate of change of #g(x) = 3 + 1/2x# from [1,8]?

1 Answer
Jim H
Jan 25, 2016

The average rate of change of function #f# on interval #[a,b]# is
#(f(b) - f(a))/(b-a)#

Explanation:

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

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

It is the ratio of the changes, it may also be written #(Deltaf)/(Deltax)# and it may be thought of as the slope of the line through the endpoints of the graph of #f# on the interval.

Algebraically it is (one version of) the difference quotient. (The quotient of the differences in #f# values and #x# values.)

For this problem you find

#(g(8)-g(1))/(8-1)#

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