EXERCISES $4\mathrm{.}9$ Newton's Method

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Newton's Method will fail to approximate the solution to $f(x)=0$ with initial guess $x_0$ when:

$x_0$ is not close to the solution of $f(x)=0.$

$f(x)$ is not a polynomial.

$f^{\text{'}}(x_0)=0.$

$f(x)$ is not differentiable at $x_0.$

$f(x)$ does not have a root.

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