Answer:
Although strictly speaking of mathematics i.e. theoritically,
t
can take any value from
{
−
∞
,
∞
]
,
however, it is essentially a physical problem related to Physics and we cannot have negative
t i.e. t
≥
0
Further, after the maximum is reached at t
=
2 (observe that first differential is h
'
(
t
)
=
−
32
t
+
64
, which is zero at t
=
2 and second derivative h
'
'
(
t
)
=
−
32 is negative and at this we have h
(
2
)
=
64
), at t
=
4
, h
(
4
)
=
0 i.e. toy rocket falls back to the ground and as such, we cannot have h
>
4
.
Hence, domain for t is [
0
,
4
]
.
tbh google
