Question

Why newton raphson diverges at inflection point?

Answer 1

For a function f(x), the point where the concavity changes from up-to-down or down-to-up are called inflection points. ... The following simulation illustrates the Newton-Raphson method converges slowly due to aninflection point occuring in the vicinity of the root.

Answer 2

causing divergence. But how come f''(x) also cannot be near zero at the vicinity of the root? What does a zero second derivative have to do with Newton's Method?