Running hardware diagnostics with Yosemite on iMac

Question

I'd like to run Hardware Diagnostics on a 2011 (maybe 2012) iMac.  Yosemite is installed.
Have disconnected everything except keyboard and mouse, shutdown, and tried starting up with the "D" key held down.  With this option, the system boots normally....no diagnostics options.
Tried with Shift D, and system boots in safe mode.
Help, please.  Thanks!

Answer 1

Thanks for the reply, Mike.
The disk has never been erased to my knowledge, although OSX has been updated with each new release.  Perhaps an old DVD with Snow Leopard might have the AHT utility?  But will it still run under Yosemite?  Is it safe to give it a try?
We're having 2 problems, and was hoping AHT could help rule out a hardware problem.  Our primary problem is that Logic Pro (up to date version) intermittently stops and gives a message that the system is too slow.  This severely impacts our ability to use the product during recording sessions.  Another problem is that we intermittently get a flashing pink and green checkerboard of pixels ...sometimes about 1 inch square, and sometimes as large as 6 inches square (GPU?)  (This issue doesn't seem to be creating any file corruption, to the best of our knowledge.)
The iMac is a 27 inch model 11,3.  We have 8GB of memory, which, when looking at Activity Monitor, usually indicates only 6.5 GB are being used.  Disk utility hasn't revealed any disk problems.  (A similar system is using about 7.8 GB, and has no similar problems with Logic). Disk is about 66% full.
If we could rule out hardware issues, we'd try to reinstall Logic Pro, and, perhaps, Yosemite.
Thanks for your help!