Question

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.

Answer 1

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