Question: Question 2 [40 marks] Consider the following data 0.3 -1.1518 -0.4 0.7028 0.5 -1.4845 0.0 0.13534 (2.1) Construct a divided-difference table for the data. (2.2)

Question 2 [40 marks] Consider the following data 0.3 -1.1518 -0.4 0.7028 0.5 -1.4845 0.0 0.13534 (2.1) Construct a divided-difference table for the data. (2.2) Use a Newton's divided-difference polynomial that interpolates all the points to approximate f(0.1). (2.3) Use the least squares approximation polynomial of degree two to approximate f(0.1) and compute the error. (Your system of normal equations must be explicit.) (2.4) Use the least-squares function of the form y = acts to approximate f(0.1) and compute the error. (2.5) Plot the graphs of the approximationg polynomials in (2.2)-(2.4). Your graphs must be proper computer produced graphs

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