Answer:
The average rate of change of a function over an interval is a measure of how the function's value changes over that interval, given by the ratio of the change in the function's value to the change in the independent variable. To find the average rate of change of a function over an interval, we need to know the function's values at two points in the interval.
In the case of the function f(x) = x^2, the interval is -4 ≤ x ≤ 0. To find the average rate of change, we need to find the difference in the function's value between two points in this interval, and divide that by the difference in the x-values.
For example, if we compare the values of the function at x = -4 and x = 0, we have:
f(-4) = (-4)^2 = 16
f(0) = 0^2 = 0
The difference in the function's value is f(0) - f(-4) = 0 - 16 = -16.
The difference in the x-values is x2 - x1 = 0 - (-4) = 4.
So the average rate of change over this interval is the difference in the function's value divided by the difference in the x-values, or -16 / 4 = -4.
In other words, the average rate of change of the function f(x) = x^2 over the interval -4 ≤ x ≤ 0 is -4, meaning that for every 4 units of change in x, the function value decreases by 16 units.
Explanation: