Problema Solution
A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by hequals
minus16tsquaredplus96tplus3952
.
What is the rocket's maximum height?
Answer provided by our tutors
h(t) = -16t^2+96t+3952
We need to find h max.
The parabolic function h(t) = -16t^2+96t+3952 has maximum (since the quotient in front of t^2 is negative -16 < 0):
h max = c - b^2/(4a), where a = -16, b = 96, c = 3952
h max = 3952 - (96^2)/(4*(-16))
h max = 4096 ft
The rocket's maximum height is 4,096 ft.