Answer:
The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:
f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4
f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6
The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.
To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."