1.40.scm

(define dx 0.00001)

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

(define tolerance 0.00001)

(define (fixed-point f first-guess)
  (define (close-enough? a b)
    (< (abs (- a b)) tolerance))

  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))

  (try first-guess))

(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)
    (+ (expt x 3) (* a (expt x 2)) (* b x) c)))

(let ((a 4)
      (b 2)
      (c 8))
  (newtons-method (cubic a b c) 1)) ; -3.9999999999968