The following describes Newton's 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 (pn−1, f (pn−1)). Derive the formula describing this method.