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 _____ feet per second.
First, we differentiate the equation for the distance so to find the velocity in feet per second (ft/s).                                f(t) = -16t² + 48t + 100 Differentiating,                              df(t)/dt = -32t + 48 The value at t = 3 is,                            df(t) / dt = -32(3) + 48 = -48 ft/s The value at t = 5 is                           df(t) / dt = -32(5) + 48 = -112 ft/s
