Question

What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0<=x<=3? Show all work.

Answer 1

Definition of average rate of change a function g(x) over an interval [a,b]:

$A = \dfrac{g(b)-g(a)}{b-a}$

Substitute your function and your interval:

$A = \dfrac{(3^6-6)-(3^0-6)}{3-0} = \dfrac{3^6-6-3^0+6}{3} = \dfrac{3^6-1}{3} = \dfrac{728}{3}$