Find the linear and quadratic interpolating polynomials

Reference no: EM131010804

Consider the data in the table

n	x_n	f(x_n)
0	1.15	0.25
1	1.2	0.5
2	1.4	0.75

a. Compute the divided differences f[x₀, x₁] and f[x₀, x₁, x₂].

b. Find the linear and quadratic interpolating polynomials using the Newton Divided Difference formulation.

c. Suppose we know that the data comes from a function f(x) that is twice differentiable and that |f"(c)| ≤ M for all c in the interval [1, 15, 1.4].

Show that the error satisfies the following inequality

|f(x) - P₁(x)| ≤ 0.01 M/ 32, for 1.15 ≤ x ≤ 1.2.

Reference no: EM131010804

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