Question

Which interval has the steepest (greatest absolute value) average rate of change?

a) (-1, 0]
b) [3, 4]
c) [-4, 0]
d) (-3, -2)

Answer 1

The interval with the steepest average rate of change is (-3, -2).

Step-by-step explanation:

The interval with the steepest average rate of change is (-3, -2).

To determine the average rate of change, we need to find the slope between the endpoints of each interval.

Considering the intervals given:

1. a) (-1, 0]: The function has a negative value that does not change with time, resulting in a constant average rate of change.
2. b) [3, 4]: The function has a gradually increasing negative value, resulting in a decreasing average rate of change.
3. c) [-4, 0]: The function has an increasing rate of negative values over time, resulting in an increasing average rate of change.
4. d) (-3, -2): The function has zero at all times, indicating a horizontal motion and a constant average rate of change.

Therefore, the interval with the steepest average rate of change is (-3, -2).