(define (square x) (* x x))

;; Newton's method

(define (deriv g)
  (lambda (x)
    (/ (- (g (+ x dx)) (g x))
       dx)))
 (define dx 0.00001)

 (define (cube x) (* x x x))

(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)
    (+ (cubed x)
       (* a (squared x))
       (* b x)
       c)))