Given f(r) = x* – 4x² + 4, use the nodes 1o = –1, x1 = 0, and x2 = 1, and valuesf(ro) = f(-1) = 1, f(x1) = f(0) = 4, and f(x2) = f(1) = 1, to construct interpolating polynomials ofdegrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and findthe actual error of each approximation of f(-0.5).%3D

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(10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of legrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find tion

(10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of legrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find tion

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

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Question

Given f(r) = x* – 4x² + 4, use the nodes 1o = –1, x1 = 0, and x2 = 1, and values
f(ro) = f(-1) = 1, f(x1) = f(0) = 4, and f(x2) = f(1) = 1, to construct interpolating polynomials of
degrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find
the actual error of each approximation of f(-0.5).
%3D

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