Prove Newton's method converges... How would you prove that Newton's Method applied to $f(x) = ax + b$ converges in one step? Would it be because the derivative of $f(x)$ is simply $a$?

Write down the formula 
$$N(x) = x-\frac{f(x)}{f'(x)}$$
for this specific function and simplify.
In the course of that procedure, you will certainly use the fact that $f'(x)=a$.
