Question 3 MUST BE SOLVED USING ANY PROGRAMMING LANGUAGE LIKE JAVA OR C++ The fastest time ever recorded in the Kentucky Derby was by a horse named Secretariat in 1973. He covered the 1 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 1:36 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. Hints and Requirements For your interpolation process use the Newton triangle of divided differences Display in a tabulated form all the in-between calculations you make and show the entire triangle Do the interpolation for the two cases below then compare and report which time prediction is more accurate at the % mile post: Case 1: ignore the start gate Case 2: include the start gate (mile post 0) to the nodes with 0 time value . . . . . Question 3 MUST BE SOLVED USING ANY PROGRAMMING LANGUAGE LIKE JAVA OR C++ The fastest time ever recorded in the Kentucky Derby was by a horse named Secretariat in 1973. He covered the 1 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 1:36 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. Hints and Requirements For your interpolation process use the Newton triangle of divided differences Display in a tabulated form all the in-between calculations you make and show the entire triangle Do the interpolation for the two cases below then compare and report which time prediction is more accurate at the % mile post: Case 1: ignore the start gate Case 2: include the start gate (mile post 0) to the nodes with 0 time value