Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c] Show that there must exist a constant d such that s(x) = d(x – c)³ on [c, b]. %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
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Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(r) = 0 on [a, c].
Show that there must exist a constant d such that s(x) = d(x – c)³ on [c, b].
Transcribed Image Text:Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(r) = 0 on [a, c]. Show that there must exist a constant d such that s(x) = d(x – c)³ on [c, b].
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