1-40.rkt

#lang racket

(define tolerance 0.00001)
(define dx 0.00001)

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

(define (average a b) (/ (+ a b) 2))

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

(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 (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) (+ (cube x) (* a (square x)) (* b x) c)))

(newtons-method (cubic 4 2 3) 1)