Exercise 3.4.6 Let be a root of f and J be an interval containing .

Exercise 3.4.6 Let ξ be a root of f and J be an interval containing ξ . Suppose that f (x) = 0 and f (x) ≥0 or f (x) ≤ 0 for x ∈ J . Explain why the Newton–

Raphson method converges monotonically to ξ from any point x0 ∈ J such that f (x0) f (x0) ≥ 0.