Question

Given the function g(x) = 6(4)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Answer 1

g(x) = 6(4)x, Section A is from x = 0 to x = 1.  Your "6(4)x" needs to be written as 

g(x) = 6(4)^x, where the " ^ " indicates exponentiation.

The average rate of change of g(x) from x= 0 to x=1 is:

              6(4)^1 - 6(4)^0         24 - 6
a.r.c. = ----------------------- = ----------- = 18 (answer)
                    1-0                         1

Now do the same thing for x = 1 to x = 2.