Newton's Method: Let f be a differentiable function on an interval I with a root in I. To approxi- mate the value of the root, accurate to d decimal places: 1. Choose a value xo as an initial approximation of the root. (This is often done by looking at a graph of f.) 2. Create successive approximations iteratively; given an approximation xn, compute the next approximation xn+1 as xn+1 = xn f(xn) f'(xn) 3. Stop the iterations when successive approximations do not differ in the first d places after the decimal point.