import util.control.Breaks._
import scala.math._

object Main extends App{

  def f(x:Double): Double = {
    sin(x)
  }

  def df(x0:Double):Double = {
    var res:Double = 0
    for(k<-0 until 3){
      res+=res
      val fx = f(x(k))
      for(j<-0 until 3){
        if(j!=k)
          res+=fx*(x(j)-x0)/(x(j)-x(k))
      }
    }
    res
  }

  var a:Double = -3
  var b:Double = 0.5
  var c:Double = (a+b)/2
  val x:Array[Double] = Array(a,c,b)
  var i =0
  var d:Double = df(i)
  breakable {
    while (b - a > 0.01) {
      d = df(i)
      if (a < d && d < c) {
        if (f(d) < f(c)) {
          b = c
          c = d
        }
        else {
          a = d
        }
      }
      else {
        if (c < d && d < b) {
          if (f(d) < f(c)) {
            a = c
            c = d
          }
          else {
            b = d
          }
        }
        else {
          break
        }
      }
      i += 1
    }
  }
  println("x: "+c)
  println("y: "+d)

}

--------------------

x: -1.8252192661843243
y: -0.9304430626040355