Answer:
The rocket will be reach its maximum height at t= 4 seconds
The maximum height 'h' = 264 feet
Explanation:
Step(i):-
Given the function 'h' = -16 t² + 128 t +8 ...(i)
Differentiating equation (i) with respective to 't' we get
...(ii)
Now equating Zero , we get

- 32 t =-128
t = 4
Step(ii):-
Again Differentiating equation (ii) with respective to 't' we get

The maximum height at t= 4
The rocket will be reach its maximum height at t= 4 seconds
The maximum height
h = -16 (4)² + 128 (4) +8
= 264
Conclusion:-
The rocket will be reach its maximum height at t= 4 seconds
The maximum height 'h' = 264