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I'm so confused i can't derive this

newton's method requires = x0 - f(x0)/f'(x0) it needs a function

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You need a function that evalates to 0 for the solution.

So how about:

$$ x^3 - 10 $$

These days, you have YouTube for explanation of Newton's method:

https://www.youtube.com/watch?v=1uN8cBGVpfs

By the way, find your typo in your question first.

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  • $\begingroup$ I don't get how calculating 10^1/3 connects to the newton method $\endgroup$
    – Ivan
    Oct 9, 2014 at 7:52
  • $\begingroup$ the above function has a 'root' at $10^{1/3}$, as desired. $\endgroup$
    – Alan
    Oct 9, 2014 at 7:56
  • $\begingroup$ Ah yes x0=2 leads to 13/6 then x1=13/6 leads to 2.15 as required =) $\endgroup$
    – Ivan
    Oct 9, 2014 at 8:27
  • $\begingroup$ Indeed, but you also have to take one step more so 2.15 would still return 2.15, to prove sufficient convergence. $\endgroup$
    – Pieter21
    Oct 9, 2014 at 8:31

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