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 _____ feet per second

Answer 1

The answer is -128
-16(6)² + 32(6) + 384 = 0
-16(4)² + 32(4) + 384 = 256
0 - 256/6 - 4 = -128

Answer 2

It is given in the question that,

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:

$f(t) = −16t^2 + 32t + 384$

At t=4seconds,

we will get

$f(4) = -16(4)^2+32(4) +384 = 256$

At t=6 seconds, we will get

$f(6)= -16(6)^2 +32(6)+384 =0$

THerefore, average rate of change is

$\frac{f(6)-f(4)}{6-4} = \frac{0-256}{2-0} = -128feet/second$

And that's the required answer .