Final answer:
The average rate of change of the function f(x) = -2x² - 3 over the interval [-3, -1] is 8.
Step-by-step explanation:
The average rate of change of a function over an interval is calculated by finding the difference in function values at the endpoints of the interval and dividing it by the difference in the input values.
In this case, the function is f(x) = -2x² - 3. The interval is [-3, -1].
First, we find the function values at the endpoints of the interval:
- f(-3) = -2(-3)² - 3 = -2(9) - 3 = -18 - 3 = -21
- f(-1) = -2(-1)² - 3 = -2(1) - 3 = -2 - 3 = -5
Then, we find the difference in function values: -5 - (-21) = -5 + 21 = 16
Finally, we find the difference in the input values: -1 - (-3) = -1 + 3 = 2
Now we can calculate the average rate of change: 16/2 = 8