I've found hundreds of posts similar to this but none have offered up any helpful explanation so here's my dilemma:
Macbook Pro 9,2 (Mid 2012) purchased in a group of 10 in the summer of 2012. Intel i5 processors. Updated as far as possible (apple won't update any farther) on Mountain Lion (10.7.2). Apple TV purchased at the same time and update to the latest Software as well (i believe it's 5.0?). Most computers have been fine for Airplay Mirroring to the Apple TV's however one specific Macbook doesn't show the Airplay Mirroring Icon in the taskbar up in the right hand side of the desktop. This computer can still connect to Apple TV via iTunes but I do not know why it wouldn't be able to Airplay Mirror. I'm wondering if there's a hardware issue? Also to be noted is that just recently the dvi stopped outputting audio (only does video now) even though it worked fine up until now. Any help is appreciated.
See > http://support.apple.com/kb/HT5404 10.7.2 is OS X Lion, and AirPlay Mirroring requires OS X Mountain Lion. On the Macs that don't show the AirPlay icon, open > About this Mac, and check Version. If it's 10.7, you have to upgrade to Mountain Lion.
If you bought those Macs after July 26th, 2012, you can upgrade them to OS X Mountain Lion for free > http://www.apple.com/osx/uptodate/