A cubic spline S is defined by:So(x) = 3(x – 1) + 2(x – 1)² – (x – 1)³if 1< x < 2%3DS(x) =1%3Ds,(x) = 4 + 4(x – 2) – (x – 2)² +(x – 2)³if 2

Given,Sx=S0x=3x-1+2x-12-x-13 if 1≤x≤2S1x=4+4x-2-x-22+13x-23…

Answered: A cubic spline S is defined by: So(x) =…

A cubic spline S is defined by: So(x) = 3(x – 1) + 2(x – 1)² – (x – 1)³ if 1< x< 2 S(x) = 1 s, (x) = 4 + 4(x – 2) – (x – 2)² +(x – 2)³ if 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

A cubic spline S is defined by:
So(x) = 3(x – 1) + 2(x – 1)² – (x – 1)³
if 1< x < 2
%3D
S(x) =
1
%3D
s,(x) = 4 + 4(x – 2) – (x – 2)² +(x – 2)³
if 2<x< 3
S is a natural cubic Spline
O False
O True

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Why is this not a cubic spline?