A drone ascends and descends along a vertical flight path. The table gives the drone’s altitude h (in meters) and an estimate of its instantaneous vertical velocity h′(t) (in m/s) at selected times t (in seconds), where 0≤t≤9.
t (s)
1
3
5
7
9
h(t) (m)
100
120
128
123
110
h′(t) (m/s)
4.0
1.2
−0.5
−2.1
−3.0
Altitude is differentiable for all t in the interval.
(a) Using the signs of h′(t), indicate the intervals on which the drone is rising and the intervals on which it is descending.
(b) Estimate the time at which the drone reaches its highest altitude during the interval 1≤t≤9. Clearly explain the reasoning that leads to your estimate.
(c) Using interpolation with the data in the table, approximate that maximum altitude.