The council and mayor, or either of them, and any officer or officers formally authorized by them, or either of them, shall have power to make investigations into the City’s affairs, to subpoena witnesses, administer oaths, and compel the production of books and papers. The council shall provide for an audit of the City’s accounts at least once a year by the State Department in charge of such work or by certified public accountant. The council may at any time provide for an examination or audit of the accounts of any officer or department of the City government and it may cause to be made any survey or research study of any subject of municipal concern.