American Century Growth Investor Class (TWCGX) N-CSR Certified annual shareholder report (management investment company)

                                                                   EX-99.906CERT


     Certification Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
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     In connection with the shareholder report of American Century Mutual Funds,
Inc. (the  "Registrant")  on Form N-CSR for the period  ending  October 31, 2004
(the "Report"),  we, the  undersigned,  certify,  pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that:

     (1)  The Report fully  complies with the  requirements  of Section 15(d) of
          the Securities Exchange Act of 1934; and

     (2)  The  information  contained  in the  Report  fairly  presents,  in all
          material respects,  the financial  condition and results of operations
          of the Registrant.


Dated:  December 27, 2004


                                     /s/ William M. Lyons
                                     ----------------------------------
                                     William M. Lyons
                                     President
                                     (chief executive officer)


                                     /s/ Maryanne L. Roepke
                                     -----------------------------------
                                     Maryanne L. Roepke
                                     Sr. Vice President, Treasurer, and
                                     Chief Accounting Officer
                                     (chief financial officer)