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#lang racket
(require "../../shared/chapter1.rkt")
(require sicp)
(define deriv (deriver 0.00001))
(define (newtons-method g guess)
(define (newton-transform f)
(lambda (x)
(- x (/ (f x) ((deriv f) x)))))
(fixed-point (newton-transform g) guess))
(define (cubic a b c)
(lambda (x)
(+ (cube x) (* a (square x)) (* b x) c)))
(define (cube-root a b c guess)
(newtons-method (cubic a b c) guess))
(cube-root 1 1 1 1)
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