5- Consider the following data points: x: 1 2 4 5 y: 2 3 5 7 a. Using the given data points, derive the Lagrange interpolating polynomial P(x) that passes through all the points. Show all steps in your calculations, including the formulation of the Lagrange basis polynomials. b. Calculate the value of the polynomial P(x) at x=3. c. Discuss how the Lagrange interpolating polynomial can be used to approximate the value of the function at points not included in the original data set. Explain the significance of the interpolation error and how it relates to the degree of the polynomial. d. Write a MATLAB script to compute and plot the Lagrange interpolating polynomial based on the provided data points. Include the original data points in the plot and show the polynomial curve.

Algebra & Trigonometry with Analytic Geometry

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