Question

Question 10 : Rockets the height in feet of a rocket t seconds after launch is modeled by the function below.Find its average speed( average rate of change) from 3 to 4 seconds.h(t)=-16t (2)+72t

Answer 1

`\begin{gathered} The\text{ average value of a function h(t) on the interval \lbrack{}a,b\rbrack{}is} \\ (1)/(b-a)\int ^b_ah(t)dt \\ \\ \text{since h represents the height, h'(t) represents the speed, and} \\ (1)/(4-3)\int ^4_3h^(\prime)(t)dt=(1)/(4-3)(h(4)-h(3))_{} \\ =h(4)-h(3) \\ =(-16(4^2)-72(4))-(-16(3^2)-72(3)) \\ =32-72 \\ =-40 \end{gathered}`