The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.
Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:
(h(2) - h(-2)) / (2 - (-2))
First, we have to find h(2) and h(-2) by substituting these values in the function:
h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5
h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5
So, the average rate of change is:
(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25
Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25