Since you can name the SARXTD started task whatever you want, the first thing you need to do is to find out what the name of it is.
If you go into SDSF, option 3.14 and in the field for Search String enter PGM=SARXTD
in the field for dataset name enter your proclib, for me it was USER.PROCLIB
the results will be any Procs that execute PGM=SARXTD.
You now have the name/names of a SARXTD started task. For me it was L1VXT122.
If you see an active started task then you can issue a modify (F) for a status.
the result was a display:
10.23.48 STC60149 SARXTD10 Security disabled
10.23.48 STC60149 SARXTD11 Accounting disabled
10.23.48 STC60149 SARXTD09 Automatic report archival enabled with specifications:
10.23.48 STC60149 SARXTD09 A/B/C//V122/D
This showed that SARXTD was active.