# 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).

.

\( x_{0} = 1.8 \)

\( x_{1} = 1.589917695 \)

\( x_{2} = 1.559713388 \)

\( x_{3} = 1.559120922 \)

\( x_{4} = 1.559120697 \)