The following describes Newtons method graphically: Suppose that f (x) exists on [a, b]

Chapter 2, Problem 2.3.15

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The following describes Newtons method graphically: Suppose that f (x) exists on [a, b] and that f (x) = 0 on [a, b]. Further, suppose there exists one p [a, b] such that f (p) = 0, and let p0 [a, b] be arbitrary. Let p1 be the point at which the tangent line to f at (p0, f (p0)) crosses the x-axis. For each n 1, let pn be the x-intercept of the line tangent to f at (pn1, f (pn1)). Derive the formula describing this method

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