Airline travel The following figure shows the ​​position function of an airliner on an out-and-back trip from Seattle to Minneapolis, where s = f(t) is the number of ground miles from Seattle t hours after take-off at 6:00 A.M. The plane returns to Seattle 8.5 hours later at 2:30 P.M. <IMAGE>
d. Determine the velocity of the airliner at noon (t = 6) and explain why the velocity is negative.

Verified step by step guidance

1. Identify the position function s = f(t) from the given figure, which represents the distance from Seattle at time t hours after take-off.
2. Determine the time t corresponding to noon, which is 6 hours after take-off (t = 6).
3. Calculate the velocity of the airliner at t = 6 by finding the derivative of the position function, v(t) = f'(t).
4. Evaluate the derivative at t = 6 to find the velocity v(6).
5. Discuss the meaning of the negative velocity, which indicates that the airliner is moving back towards Seattle at that time.