Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 4, is less than or equal to, x, is less than or equal to, 64≤x≤6.
x f(x)
3 3
4 9
5 27
6 81
7 243
To find the average rate of change over the interval 4 ≤ x ≤ 6, we need to calculate the total change in the function f(x) over this interval and then divide by the change in x.
First, let's find the change in the function f(x) over the interval 4 ≤ x ≤ 6:
f(6) - f(4) = 81 - 9 = 72
Next, let's find the change in x over the interval 4 ≤ x ≤ 6:
6 - 4 = 2
Now, we can calculate the average rate of change:
Average rate of change = total change in f(x) / change in x
Average rate of change = 72 / 2
Average rate of change = 36
Therefore, the average rate of change of the function over the interval 4 ≤ x ≤ 6 is 36.