Question

The altitude (in feet) attained by a model rocket t seconds into flight is
given by the function

h(t) = -1/3t^3 + 4t^2 + 20t + 2,for t _> 2

a)Find the maximum altitude attained by the rocket.

b)Why does it not make sense to use this function after t = 16
seconds? Use the graph of h(t) that is given

Answer 1

dh/dt = -t^2 + 8t + 20
= -(t-10)(t+2)
max h when t=10, h(10) = 806/3

h(16)=0, so the rocket has landed by then. No change in h thereafter.