A Hint on decomposing Newton's Method

The real art to programming is learning how to decompose a large task into smaller, more manageable ones.

For implementing Newton's Method for finding roots, I decomposed the problem into 3 functions; here are the comments for them.

;; (estimate-slope f x)
;; Given a function f:R->R, and a real number x,
;; find (roughly) the slope of f at x.
;;
(define estimate-slope
   ;...

;; (crosses-at x0 y0 m)
;; given a point (x0,y0) and a slope m,
;; calculate where the line so determined
;; crosses the x-axis.
;;
;; This code assumes m is not zero!
;;
(define crosses-x-at
   ;...

;; (newton f x0)
;; Starting at x0, iterate f by newton's method
;; until we are close to root.
;;
(define newton
    ;...