;; Teachpack: graphing.ss 
;; Language: Intermediate or higher

#| Template
1. Trivial case:
Problem is solved if f is 0 at the point tested.
2. Divide:
To generate a new problem, cut the interval in half.  Look in the
half where the graph crosses the x-axis.
3. Conquer:
Simply return the first point found where f is 0.
|#

;; Warning: As currently written, this algorithm may never terminate.

;; find-zero : Number Number (Number -> Number) -> Number
;; to find a zero for f between left and right 
(define (find-zero left right f)
  (local [(define mid (/ (+ left right) 2))]
    (cond
      [(= (f mid) 0) mid]
      [(> (f left) 0 (f mid)) (find-zero left mid f)]
      [(< (f left) 0 (f mid)) (find-zero left mid f)]
      [else (find-zero mid right f)])))

;; A test of the program

;; f : Number -> Number
(define (f x) (+ (* x x) x -2))

(graph-fun f 'blue)
(find-zero 0 4 f)

;; Another test of the program

;; g : Number -> Number
(define (g x) (+ (* x x x) (* -8 x x) (* 19 x) -12))

; (graph-fun g 'red) ; <--- uncomment
; (find-zero 0 5 g) ; <--- uncomment