plektix

You can calculate the derivatives (to all orders) of exp(-1/x^2) using the chain rule and other basic calculus rules. Then you just need to check that these derivatives are equal to zero at x=0 (i.e. the derivative coming from the left equals the derivative coming from the right.) This is all that is needed to prove that derivatives of all orders exist.

I would rather see the LGBT people reframe their appear for social acceptability around the concept of kin selection.

No civil rights campaign has built itself around genetic or evolutionary arguments. Most people don't grok kin selection, but they do grok basic human rights.

But for them to make those in-your-face claims

We're only in your face when it's the only way for us to be heard. As buttacup and visceral both mentioned, most LGBT people just want to live our lives unhindered. But we'll get in people's faces if it's necessary to draw attention to the injustices we face.

that their persecution is somehow worse than everyone else's

I have not heard a single LGBT activist claim this. In fact, many of us consider the fight for LGBT rights as part of a broader struggle for human rights for all people. The fact is that we face many kinds of discrimination, though the situation has improved greatly in my lifetime. Whether our situation is better or worse than other disadvantaged groups is completely immaterial.

Instead they should emphasize the benefits of having LGBT people round, I think.

Actually, we do this. A large part of our campain is pointing out that we are productive members of society, more so than many people realize.