Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 15, is less than or equal to, x, is less than or equal to, 3015≤x≤30.
x f(x)
0 58
15 40
30 22
45 44
60 −14
To find the average rate of change over the interval 15 ≤ x ≤ 30, we can use the formula:
Average rate of change = (f(30) - f(15)) / (30 - 15)
First, find f(30) and f(15) using the table:
f(30) = 22
f(15) = 40
Now, substitute the values into the formula:
Average rate of change = (22 - 40) / (30 - 15)
Average rate of change = -18 / 15
Average rate of change = -6/5
Therefore, the average rate of change of the function over the interval 15 ≤ x ≤ 30 is -6/5 or -1.2.