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Answer:
see attachment
Step-by-step explanation:
The iterator for Newton's method gives the next approximation (x') as ...
x' = x -g(x)/g'(x) . . . . . where g'(x) is the derivative of g(x)
We have defined g(x) = x^3+x+3, the function we want the zero of. We have defined the iteration function to be f(x).
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Additional comment
Modern graphing calculators not only make the iteration trivially simple, they also give a first approximation good to 2 or 3 decimal places in many cases.
