Newton method in racket

newton.rkt

;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname newton-method) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))

;; newton-method: (X -> Y) (X -> Z) number number -> number
;;
;; Makes use of the newton method to calculate the f(x) = 0
;;
;; Example:
(define (newton-method fct fct-abl x delta)
  (local [
          (define x1 (- x (/ (fct x) (fct-abl x))))
          (define difference (- x x1))]
    (cond
      [(<= difference delta) x1]
      [else (newton-method fct fct-abl x1 delta)])))

;; Tests
(check-expect (newton-method (lambda (x) (sqr x)) (lambda (x) (* 2 x)) 2 2) 1)
(check-expect (newton-method (lambda (x) (sqr x)) (lambda (x) (* 2 x)) 2 1) 1)
(check-expect (newton-method (lambda (x) (sqr x)) (lambda (x) (* 2 x)) 2 0.5) 0.5)