First of all, Sean, if you're in a 172 taking off from a short strip with a tailwind, I don't think you are an instructor. Secondly, an engine failure at rotation makes Vy or Vx quite moot, you're landing straight ahead or you're an idiot. (All due respect). I climb at 70 in the 172, 90 in my Skylane.
AF
I'm not sure how to interpret your post, but maybe you should re-read my last post, or perhaps the whole thread.
I have never said that I take off from short strips in tailwinds, neither are we talking about engine failures on rotation. We are talking about engine failures on climb out with no runway remaining.
EDIT: and by the way, one question for you AF:
Why do you cllimb out at 70 in your C172? I am assuming that is somewhere between Vx and Vy, correct?