## Newton's Method Solving an Equation February 10

What would be the Newton's method in the form $x_{k+1}=g(x_k)$ to solve the equation $$f(x)=x^bx+b^2-d^2=0$$ in which both $b>0,d>0$ are parameters? Additionally, I need to show that $|g'(x)|\le 1/2$ whenever $|x-b|\ge d/\sqrt{2}$ and also that $