Question: Can you help me understand part b) why is it that to find a1 we plug in 2 and to find a2 we plug in

Can you help me understand part b) why is it that to find a1 we plug in 2 and to find a2 we plug in 4

3. You are given the following table of three values of function f: f(x) 2 4 5 5 (a) (6 points) Find the Lagrange polynomial P3 for the data from the table. (b) (10 points) Let us consider Lagrange interpolating polynomial P3 in Newton's form: P3(x) = 1 + aix + a2x(x - 2) + a3x(x -2)(x -4). Find a1 and a2. (c) (4 points) Natural cubic spline interpolant for the data from the table is 0.034091x-3 - 1.3636x + A for 0

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