Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0, is less than or equal to, x, is less than or equal to, 300≤x≤30. xx f, of, xf(x) 00 5151 66 4242 1212 3333 1818 2424 2424 1515 3030 66
Question
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0, is less than or equal to, x, is less than or equal to, 300≤x≤30. xx f, of, xf(x) 00 5151 66 4242 1212 3333 1818 2424 2424 1515 3030 66
Solution
The average rate of change of a function over an interval [a, b] is given by the formula:
(f(b) - f(a)) / (b - a)
From the table, we can see that when x = 0, f(x) = 51 and when x = 30, f(x) = 6.
So, substituting these values into the formula, we get:
(6 - 51) / (30 - 0) = -45 / 30 = -1.5
So, the average rate of change of the function over the interval 0 ≤ x ≤ 30 is -1.5.
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