We'll return the minimum and maximum words in a two element String array minMax[0] hold the minimum and minMax[1] hold the maximum. 

<Brute force search for minimum and maximum>=
public String[] naiveMinMax(String[] words) {
  String[] minMax = new String[2]; 
  minMax[0] = words[0];
  minMax[1] = words[0];
  for (int i = 1; i < words.length; i++) {
    if (words[i].compareTo(minMax[0]) < 0) { 
      minMax[0] = words[i]; 
    }
    else if (words[i].compareTo(minMax[1]) > 0) { 
      minMax[1] = words[i]; 
    }
  }
  return minMax;
}