Use Newton's method to approximate the root of the equation

x^3=113 x+226

that belongs to the interval (6,12 ).

Start with x0=12 and perform three iterations, i.e., find x1,x2, and x3.

Calculate |x0−x1|,|x1−x2|, and |x3−x2|.

1. Use Newton's method

where the function f has a positive leading coefficient so that f(x)= ???