Tail recursive functions written in Scala

scala-tail-recursion

/**
 * Proprietary work of Alex Ehrnschwender
 */

  def sum(xs: List[Int]): Int = {
    var i = 0
    if (xs.isEmpty) i else i + xs.head + sum(xs.tail)
  }

  def max(xs: List[Int]): Int = {    
    def comparator(i: Int, j: List[Int]): Int = {
        if(j.tail.isEmpty) i else
          if(i > j.tail.head) comparator(i, j.tail) else
            max(j.tail)
    }
    if(!xs.isEmpty && xs.tail.isEmpty) xs.head else
      if(xs.head > xs.tail.head) comparator(xs.head, xs.tail) else
        max(xs.tail)
  }

I searched google for a scala tail-recursive version of list insert function and landed on this page. But I have to point out your implementation of "sum" is not tail-recursive.
You should use a helper function and an accumulator to achieve it.

The tail recursive version of sum function is:

def sum(xs: List[Int]): Int = {
  def loop(sum: Int, xs: List[Int]): Int = {
    if (xs.isEmpty) sum
    else loop(sum + xs.head, xs.tail)
  }
  loop(0, xs)
}