Problem 1. (Module 6) The measured velocity of a moving object is recorded in Table 1. It is desired to estimate the velocity at t= 12 seconds, between the last two data points where there exists a relatively large gap. a) Find the Lagrange interpolating polynomial (P) that goes through all 5 points. b) Find the interpolated values at t= 12 by interpolating polynomial. c) Plot the entire data and interpolating polynomial including the interpolated point. Note: the Matlab program for Example #3, Module 6 can be used (Lagran_example_.m with lagran.m function) Table 1 Velocity (v), ft/s Time (t), s 120 564 873 1012 1670 Put your answer in this field: P= P(12)= Paste the plot here