Consider a smooth function f(x) with the following values. 3 -1 1 2 x f(x) -1 0 3 -1 (a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form (b) Use divided differences to find the polynomial p(a) interpolating f(x) in Newton forr (c) Assuming all derivatives of f available, give expression of the interpolation er are an -1, 2 f(t) - p(t) for some t E

Consider a smooth function f(x) with the following values. 3 -1 1 2 x f(x) -1 0 3 -1 (a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form (b) Use divided differences to find the polynomial p(a) interpolating f(x) in Newton forr (c) Assuming all derivatives of f available, give expression of the interpolation er are an -1, 2 f(t) - p(t) for some t E

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 50E

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