Which function has the greatest rate of change on the interval from x = 3 pi over 2 to x = 2π? a) f(x) b) g(x) c) h(x) d)all three functions have the same rate of change.

The average rate of change for the function f(x) can be calculated from the following equation


By applying the last formula on the given equations 
(1) the first function f
from the table f(3π/2) = -2   and   f(2π) = 0
∴ The average rate of f =

(2) the second function g(x)
from the graph g(3π/2) = -2   and   g(2π) = 0
∴ The average rate of g =

(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
   h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h =

By comparing the results, The function which has the greatest rate of change is h(x)


So, the correct answer is option C) h(x)