Suppose that f is a continuous nonnegative function onthe interval [a, b], n is even

Chapter 7, Problem 54

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Suppose that f is a continuous nonnegative function on the interval [a, b], n is even, and [a, b] is partitioned using \(n+1\) equally spaced points,\(a=x_{0}<x_{1}<\cdots<x_{n}=b\). Set \(y_{0}=f\left(x_{0}\right), y_{1}=f\left(x_{1}\right), \ldots, y_{n}=f\left(x_{n}\right)\). Let \(g_{1}, g_{2}, \ldots, g_{n / 2}\) be the quadratic functions of the form \(g_{i}(x)=A x^{2}+B x+C\) so that
(cont.)

Equation Transcription:

 

 

Text Transcription:

n+1

a=x_0 < x_1 < times times times < x_n = b

y_0=f(x_0), y_1=f(x_1),...,y_n=f(x_n)

g_1,g_2,...,g_n/2

g_i (x) = Ax^2+Bx+C