(load "1.35.txt") ; for fixed-point

(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))

; x^3 + ax^2 + bx + c = 0
(define (cubic a b c)
  (lambda (x)
    (+ (* x x x) (* a x x) (* b x) c)))

; (x - 5)(x^2 + 1) = x^3 - 5x^2 + x -5
; 1 ]=> (newtons-method (cubic -5 1 -5) 1)
; 
; ;Value: 5.000000000004096