Answer:
Explanation:
The average rate of change of a function over an interval is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a and b are the endpoints of the interval.
For the function f(x) = -0.5x^2, we have:
f(-3) = -0.5(-3)^2 = -4.5
f(3) = -0.5(3)^2 = -4.5
So the average rate of change of f(x) over the interval -3 < x < 3 is:
average rate of change = (f(3) - f(-3)) / (3 - (-3))
average rate of change = (-4.5 - (-4.5)) / 6
average rate of change = 0
For the function g(x) = -1.5x^2, we have:
g(-3) = -1.5(-3)^2 = -13.5
g(3) = -1.5(3)^2 = -13.5
So the average rate of change of g(x) over the interval -3 < x < 3 is:
average rate of change = (g(3) - g(-3)) / (3 - (-3))
average rate of change = (-13.5 - (-13.5)) / 6
average rate of change = 0
Therefore, the average rates of change for both f(x) = -0.5x^2 and g(x) = -1.5x^2 over the interval -3 < x < 3 are 0. This means that the functions are constant over this interval, and their slopes are not changing.