Highway travel A state patrol station is located on a straight north-south freeway. A patrol car leaves the station at 9:00 A.M. heading north with position function s = f(t) that gives its location in miles t hours after 9:00 A.M. (see figure). Assume s is positive when the car is north of the patrol station. <IMAGE>
c. Find the average velocity of the car over the interval [1.75, 2.25]. Estimate the velocity of the car at 11:00 A.M. and determine the direction in which the patrol car is moving.

Verified step by step guidance

1. Identify the time interval for which you need to find the average velocity, which is from t = 1.75 hours to t = 2.25 hours after 9:00 A.M.
2. Use the position function s = f(t) to find the positions of the patrol car at the endpoints of the interval: calculate f(1.75) and f(2.25).
3. Apply the formula for average velocity over the interval [1.75, 2.25], which is given by the formula: average velocity = (f(2.25) - f(1.75)) / (2.25 - 1.75).
4. To estimate the velocity of the car at 11:00 A.M., which corresponds to t = 2 hours, evaluate the position function at that time: find f(2).
5. Determine the direction of the patrol car's movement by analyzing the sign of the velocity, which is the derivative of the position function, v(t) = f'(t). If v(t) > 0, the car is moving north; if v(t) < 0, it is moving south.