A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation ℎ () = - 162 + 64, where is the time in seconds. Determine the domain, using interval notation, for this function in the given context.

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