A rocket is fired into the air, and its height in meters at any given time t can be calculated using the formula h(t) = 1600 + 4.9t^2. Find the maximum height of the rocket and the time at which it occurs.

Answer 1

First, find the first derivative of the height function h(t):

h'(t) = d(1600 + 4.9t^2)/dt = 9.8t

To find the maximum height, set h'(t) = 0 and solve for t:

9.8t = 0
t = 0

The maximum height occurs at t = 0. Now, find the height at this time:

h(0) = 1600 + 4.9(0)^2 = 1600

The maximum height of the rocket is 1600 meters, and it occurs at time t=0.