You cannot say if there is a peak outside the datapoints if you don't have any additional information about the function. You have to confine the possible functions to some special class to have an exact solution. For instance - you can assume that it is a polynomial - than there is exactly one polynomial with the lowest range that will fit to the data. Still finding it's extrema might be a bit difficult for range greater than 5 (you would have to solve the derivative of the polynomial).