Question: Given P(x), where P describes the kth Lagrange polynomial that interpolates f at k+ 1 points:
A function is being interpolated at the points x_0 = 0.0, x_1 = 0.2, x_2 = 0.4, x_3 = 0.6, x_4 = 0.8, and x_5 = 1.0. It has been determine that P_1,3,4,5 (0.5) = 3.0 and P_1,2,3,4(0.5) = 4.0. Calculate P_1,2,3,4,5(0.5).