Step-by-step explanation:
the extreme values of a function happen at the zeros of the first derivation of that function.
f(t) = -16t² + 72t
f'(t) = -2×16t + 72 = -32t + 72
0 = -32t + 72
32t = 72
t = 72/32 = 2.25 seconds
f(2.25) = -16(2.25)² + 72×2.25 = -16×5.0625 + 72×2.25 =
= -81 + 162 = 81 ft
so, the rocket reaches its maximum height of 81 ft after 2.25 seconds of flight.
