#lang sicp

(define tolerance 0.0001)
(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) 
       tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))
(define dx 0.00001)
(define (deriv g)
  (lambda (x)
    (/ (- (g (+ x dx)) (g x))
       dx)))
(define (newton-transform g)
  (lambda (x)
    (- x (/ (g x)
            ((deriv g) x)))))
(define (newtons-method g guess)
  (fixed-point (newton-transform g)
               guess))
(define (cubic a b c)
  (lambda (x) (+ (* x x x) (* a x x) (* b x) c)))

(newtons-method (cubic -6 3 5) 5.0)
(display "5.2465513645585649... (exact)")