A car traveling along a straight road is clocked at a number of points. The data from the observations are given in the following table, where the time is in seconds, the distance is in feet, and the speed is in feet per second. Time 0 3 5 8 13 Distance 0 225 383 623 993 Speed 75 77 80 74 72 (a) Compute a Hermite interpolating polynomial for the data. (b) Use your polynomial from part (a) to predict the position (distance) of the car and its speed when t=10 seconds. (c) Determine whether the car ever exceeds the 55 mph speed limit on the road. If so, what is the first time the car exceeds this speed? (d) What is the predicted maximum speed for the car? NOTES: Speed is the derivative of distance. 55 ( miles )/( hour ) =55 ( miles )/( hour ) ×(5280 feet )/( mile ) ×(1 hour )/(3600 seconds ) ≈80.67 ( feet )/( second ) | Numerade