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1. Construct the Lagrange interpolating polynomial for f(x)=ex=y(x) for the set of nodes x1={x0,x1,x2,x3,x4}={1,21,0,21,1} in the interval x[1,1]. Find p4(x) for the set of nodes specified. Plot the function, the interpolating polynomial and the error on the interval defined by the nodes. 2. Table below gives the actual thermal conductivity data for iron. Construct a least square fit to this data and plot both curve and raw data. How well does your curve represent the data? For this question, construct a Python program without using any special library from numpy or scipy