Question 4: 18 Marks Consider the following data: -0.5 5 0 15 0.5 9 3 1.5 1 (4.1) Set up a difference table through third differences (4.2) What is the minimum degree that an interpolating polynomial, that fits all five data (3) (4.3) Give the (forward) Newton-Gregory polynomial that fits the data points with X values (3) (4.4) Compute an approximate bound for the error in the approximation to f(1.25) in (4.3) (3) (4.5) Compute f(1.25) using the Lagrange interpolating polynomial through the data points (3) (4.6) Construct the natural cubic spline for the last four data points points exactly, can have? Explain. 0.5, 1, and 1.5. Then compute f(1.25). using Newton's forward interpolating polynomial with X values 0.5, 1, and 1.5 Question 4: 18 Marks Consider the following data: -0.5 5 0 15 0.5 9 3 1.5 1 (4.1) Set up a difference table through third differences (4.2) What is the minimum degree that an interpolating polynomial, that fits all five data (3) (4.3) Give the (forward) Newton-Gregory polynomial that fits the data points with X values (3) (4.4) Compute an approximate bound for the error in the approximation to f(1.25) in (4.3) (3) (4.5) Compute f(1.25) using the Lagrange interpolating polynomial through the data points (3) (4.6) Construct the natural cubic spline for the last four data points points exactly, can have? Explain. 0.5, 1, and 1.5. Then compute f(1.25). using Newton's forward interpolating polynomial with X values 0.5, 1, and 1.5