The City Council shall have the power, should it deem fit to do so, to appoint a special attorney for the tax department of said city to be known as the “tax attorney,” whose duty it shall be, under the supervision of the city attorney, to press for collection and payment all unpaid and delinquent taxes due the City of Fort Worth and to prosecute suits thereon in courts of competent jurisdiction, whenever instructed so to do; or the City Council shall have the power to require the performance of such work by the corporation counsel, the prosecuting attorney, or other assistant to the corporation counsel.