Question

The rate of change R, in kilometers per hour, of the altitude of a hot air balloon is given by R(t)=t^3-4t^2+6 for time on the interval [0,4], where t is measured in hours. Assume the balloon is on ground level.

What is the maximum altitude of the balloon during the interval [0,4]?

Answer 1

Find dR/dt, set equal to zero, find time. PUt that in the original equation for altitude.

R'=3t^2-8t=0
t(3t-8)=0

t=0, t= 8/3 sec

Rmax=R(8/3)= you do it.

Answer 2

9.727