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

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