/* Precondition: The signs of f(a) and f(b) are different */
double findRootBetween(double a, double b){
  double l = a, u = b;
  while (!isSmallNumber(f(middleOf(l,u)))){ 
    if(sameSign(f(middleOf(l,u)), f(u)))
      u = middleOf(l,u);
    else 
      l = middleOf(l,u);
  }
  return middleOf(l,u);
}