For ex. 18 (Answer: https://www.chegg.com/homework-help/Numerical-Analysis-10th-edition-chapter-3.3-problem-18E-solution-9781305253667)

Do the interpolation for the following two cases then compare and report which speed prediction is more accurrate

Case I: Ignore the start gate

Case II: include the start gate to the nodes with 0 speed value (mile post = 0)

18. The fastest time ever recorded in the Kentucky Derby was by a horse named Secretariat in 1973. He covered the l mile track in 1:59 (1 minute and 59.4 seconds). Times at the quarter-mile, half-mile. and mile poles were 0.25, 0 : 49, and i :36 . a. Use interpolation to predict the time at the three-quarter mile pole and compare this to the actual time of 1:13 b. Use the derivative of the interpolating polynomial to estimate the speed of Secretariat at the end of the race. 18. The fastest time ever recorded in the Kentucky Derby was by a horse named Secretariat in 1973. He covered the l mile track in 1:59 (1 minute and 59.4 seconds). Times at the quarter-mile, half-mile. and mile poles were 0.25, 0 : 49, and i :36 . a. Use interpolation to predict the time at the three-quarter mile pole and compare this to the actual time of 1:13 b. Use the derivative of the interpolating polynomial to estimate the speed of Secretariat at the end of the race