# The Newton-Raphson Iteration

Calculus Level 3

Suppose you need the cube root of 3.79, but your calculator only does the four basic operations. You can use the Newton-Raphson method to calculate the root to any amount of accuracy needed.

$\large x_{n+1} = x_{n} - \frac{ f(x_{n})}{f'(x_{n})}$

Find f(x).

.

$$x_{0} = 1.8$$

$$x_{1} = 1.589917695$$

$$x_{2} = 1.559713388$$

$$x_{3} = 1.559120922$$

$$x_{4} = 1.559120697$$

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