Aball 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 + 34t + 546 the average rate of change of f(t) from t = 5 seconds to t = 7 seconds is feet per second.

We have the following function:
 f(t) = −16t2 + 34t + 546
 By definition, the average rate of change is:
 Avr = (f (t2) - f (t1)) / (t2 - t1)
 We have then:
 For t1 = 5:
 f (5) = -16*(5)^2 + 34*(5) + 546
 f (5) = 316
 For t2 = 5:
 f (7) = -16*(7)^2 + 34*(7) + 546
 f (7) = 0
 Substituting values:
 Avr = (0 - 316) / (7 - 5)
 Avr = -158
 
 The average rate of change of f (t) from t = 5 seconds to t = 7 seconds is -158 feet per second.