Let x0, x1, ..., Xn be distinct points on the interval [a, b], where Xo

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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4.
Let X₁, X₁, Xn be distinct points on the interval [a, b], where
Xo <x₁ < x₂ << Xn
and let f be defined in [a, b]. Prove that there exists a polynomial P₁(x) such that
f(x)) = P₁ (x))
for j = 0,1,..., n.
Prove that the polynomial P(x) in question number (3) is unique.
Transcribed Image Text:4. Let X₁, X₁, Xn be distinct points on the interval [a, b], where Xo <x₁ < x₂ << Xn and let f be defined in [a, b]. Prove that there exists a polynomial P₁(x) such that f(x)) = P₁ (x)) for j = 0,1,..., n. Prove that the polynomial P(x) in question number (3) is unique.
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