abdullahhamid2
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- Dec 15, 2020
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Suppose f(x) is a given function, we are given two points (xi–1, f(xi-1)) and (xi, f(xi)).
(a) Find the Lagrange form of the degree 1 interpolating polynomial p(x) that passes through these points; that is, p(x) is a line that approximates f(x).
(b) Find the Lagrange form of the degree 1 interpolating polynomial q(y) that passes through these points, but instead of approximating f, q(y) is a line that approximates the inverse f-1(y).
(c) Using the result from part (b), show that xi+1 = q(0) is one step of the secant method for approximating a root of f(x) = 0.
(a) Find the Lagrange form of the degree 1 interpolating polynomial p(x) that passes through these points; that is, p(x) is a line that approximates f(x).
(b) Find the Lagrange form of the degree 1 interpolating polynomial q(y) that passes through these points, but instead of approximating f, q(y) is a line that approximates the inverse f-1(y).
(c) Using the result from part (b), show that xi+1 = q(0) is one step of the secant method for approximating a root of f(x) = 0.