(define (cube x)

(* x x x))

(define tolerance 0.00001)

(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 dx 0.00001)

(define (deriv g)

(lambda (x)

(/ (- (g (+ x dx)) (g x))

dx)))

(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 0 0 -8) 1)

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