Answer:
To find the average rate of change of the quadratic function p on the interval 0 ≤ x ≤ 4, we can calculate it separately for each interval and then average the results.
On the interval 0 ≤ x ≤ 2, we are given that the average rate of change of p is -4. This means that for every 1 unit increase in x in this interval, the value of p decreases by 4 units.
On the interval 2 ≤ x ≤ 4, we are given that the average rate of change of p is -1. This means that for every 1 unit increase in x in this interval, the value of p decreases by 1 unit.
Now, to calculate the average rate of change of p on the interval 0 ≤ x ≤ 4, we need to consider the combined change in p over both intervals. Since the intervals are consecutive, the change in p from the end of the first interval to the start of the second interval contributes to the overall average rate of change.
The change in p from the end of the first interval to the start of the second interval is -4 * (2 - 0) = -8 units. This means that the value of p decreases by 8 units as x goes from 2 to 2.
The total change in p over the entire interval 0 ≤ x ≤ 4 is the sum of the changes in both intervals, which is -8 + (-1 * (4 - 2)) = -8 - 2 = -10 units. This means that the value of p decreases by 10 units as x goes from 0 to 4.
Since the interval is 4 units long (4 - 0), the average rate of change of p on the interval 0 ≤ x ≤ 4 is -10 / 4 = -5/2 or -2.5.
Therefore, the average rate of change of p on the interval 0 ≤ x ≤ 4 is -2.5.