Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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single root of a cubic function

As it can be shown that the function f(x)=3x^3-9x+1 has a single root in the interval abierto (0,1). Try to solve using Newton Raphson method, but that is more than a demonstration calculation