(def tolerance 0.00001)
(defn fixed-point [f first-guess]
  (defn close-enough? [v1 v2]
    (< (math/abs (- v1 v2))
       tolerance))
  (defn try-it [guess]
    (let [next (* 0.5 (+ guess (f guess)))]
      (if (close-enough? guess next)
        next
        (try-it next))))
  (try-it first-guess))

(def dx 0.00001)
(defn deriv [g]
  (fn [x] (/ (- (g (+ x dx)) (g x)) dx))) 

(defn newton-transform [g]
  (fn [x] (- x (/ (g x) ((deriv g) x)))))
(defn newtons-method [g guess]
  (fixed-point (newton-transform g) guess))

(defn cubic [a b c]
  (fn [x]
    (let [cub (* x x x)
          qua (* a x x)
          sing (* b x)]
      (+ cub qua sing c))))

(print (newtons-method (cubic 5 3 -1) -10))