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I'm trying to find an approximation for $11^{\frac{1}{3}}$ by using Newton's method using $x_0 = \frac{3}{2}$. Now my problem only tells me to use a "suitable" function and that threw me off quite a bit. I know this is kind of a weak question, but could anyone explain/give me a hint how I can find a suitable function?

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    $\begingroup$ Newton's method finds roots, so to use it you need some function which has $11^{1\over 3}$ as a root. But you also need one that evaluting doesn't require you to already know $11^{1\over 3}$. littleO's answer gives the obvious choice. $\endgroup$ – Paul Sinclair Oct 22 '15 at 22:06
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You want to find a root of the polynomial $f(x) = x^3 - 11$.

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