Two curious calculus students recorded the speedometer readings every 2 minutes on their way to school one morning. Their data is given in the table below:
t (minutes) 0 2 4 6 8 10 12 14 16
v(t) (mph) 50 52 51 48 46 45 48 55 60
A. Approximate the average speed over the time interval 0 st s 12 using a trapezoidal approximation with subintervals of length At= 2 minutes. (3 points) B. If the function f(t) =.03.x-.5x² +1.4x + 51 is used to model the velocity at time t, find the average value of fover the time interval 0 st s 14 minutes. (3 points)
C. Using function f(t) from part (B), find f'(8). Round your answer to the nearest tenth. (1 point)
D. Explain the meaning of your answer in part (C) in terms of the problem. (2 points)