Ok so newtons method is stated to be have quadratic convergence when $\displaystyle f'(x)!=0$ (Doesnt Equal Zero) and of course a couple other conditions.

My Question how can we improve the convergence of newtons method when $\displaystyle f'(x)=0$

Newtons Method:

$\displaystyle x_n=x_(_n_-_1_) - f(x_(_n_-_1_))/f'(x_(_n_-_1_))$

As you can see if the derivative of f is equal to zero then we are screwed. Ha and I dont remb how to do it. THank you