Question: suppose fin C^2[a,b] is strictly increasing, and has a root p in [a,b]. Then Newton's method applied to f(x) = 0 will converge to p

suppose f\in C^2[a,b] is strictly increasing, and has a root p in [a,b]. Then Newton's method applied to f(x) = 0 will converge to p for any initial p_0 \in [a,b]

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