Please show all the work by hand. Thanks

5. (20 pts) The fastest time ever recorded in the Kentucky Derby was by a horse named Secretariat in 1973. He covered the 1.25 mile track in 1 minute and 59.4 seconds. Times at the quarter-mile, half- mile, and mile poles were 25.2 seconds, 49.2 seconds, and 1:36.4 minutes. (a) Create an interpolating polynomial by hand (using either Lagrange Interpolating Polynomials or Newton's Divided Differences) 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.