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Moderate

Understand Why Newton's Method Can Fail

SVCALC-JELTCA

Consider the function $f(x)=\sqrt[3]{x}$. Why will Newton's Method fail on this function for all initial test points except $x_0=0$?

A

The function has no roots.

B

Subsequent iterations will increase to $\infty$.

C

Subsequent iterations will drift further from $0$.

D

In each iteration, $x_{n+1}=-x_n$.