Topic: interpolation and polynomial approximation 1 + 2x - x3 , on [ 0 , 1] f(x) = { 2 + a(x-1) + b(x-1)2 + c(x-1)3 , on [1,2] from the functions piecewise function given above, find the values of a,b,c that will make the f(x) a natural cubic spline on [ 0,2]

Topic: interpolation and polynomial approximation 1 + 2x - x3 , on [ 0 , 1] f(x) = { 2 + a(x-1) + b(x-1)2 + c(x-1)3 , on [1,2] from the functions piecewise function given above, find the values of a,b,c that will make the f(x) a natural cubic spline on [ 0,2]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 24E

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Question

Topic: interpolation and polynomial approximation

1 + 2x - x³, on [ 0 , 1]
f(x) = {
2 + a(x-1) + b(x-1)² + c(x-1)³ , on [1,2]

from the functions piecewise function given above, find the values of a,b,c that will make the f(x) a natural cubic spline on [ 0,2]

Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.

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