Final answer:
To find the average rate of change over an interval, subtract the function values at the endpoints and divide by the change in x.
Step-by-step explanation:
To find the average rate of change over an interval, we need to calculate the change in the function values divided by the change in the input values. In this case, the interval is -2 ≤ x ≤ 0. To calculate the average rate of change, we need to find f(x) at the endpoints of the interval and subtract the function values. Then, we divide by the change in x.
For x = -2, f(x) = -3.5(-2)² + 6 = 19. For x = 0, f(x) = -3.5(0)² + 6 = 6. The change in f(x) is 6 - 19 = -13, and the change in x is 0 - (-2) = 2. Thus, the average rate of change over the interval is -13/2 = -6.5.