Question

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:
f(t) = −16t2 + 32t + 384

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is :blank: feet per second.

Answer 1

The answer for the blank is simply -128

Answer 2

For this case we have the following function:
 f (t) = -16t2 + 32t + 384
 By definition we have to:
 The average rate of change:
 AVR = (f (t2) - f (t1)) / (t2 - t1)
 Where,
 For t1 = 4
 f (4) = -16 * (4) ^ 2 + 32 * (4) + 384
 f (4) = 256
 For t2 = 6
 f (6) = -16 * (6) ^ 2 + 32 * (6) + 384
 f (6) = 0
 Substituting values we have:
 AVR = (0 - 256) / (6 - 4)
 AVR = -128
 Answer:
 The average rate of change of f (t) from t = 4 seconds to t = 6 seconds is -128 feet per second.