I want to find a number r such that r^2 = e^r . Of course, this is equivalent to either r = e ^(r/2) or r = e^ (r/2) (which one?).

(a) How can I use the Newtons method to find r? Propose a function f whose root coincides with the number r that I want to find.

(b) Propose an initial approximation x0 that guarantees convergence (explain your choice of x0)

Please provide all steps and details, it would be greatly appreciated!