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  • A function f(x)=ex passes through the points (0,1), (0.6,1.8221), 1.2,3.3201) and (1.8,6.0496). Answer the following Questions:

    a. If the function f(x) is interpolated by a polynomial for x∈[−0.5,1.5], which points can be chosen as nodes?

    b. Now, we would like to interpolate this function by a quadratic polynomial p2(x) by choosing the first three points as nodes. Compute the Lagrange bases for the interpolating function p2(x).

    c. Using the bases you found, write down the algebraic expression of p2(x), and simply the expression to write the result in natural basis.

    d. Verify that at the nodal points |f(x)−p2(x)|=0.

    e. Compute the error |f(0.75)−p2(0.75)|.

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