What am I missing, not least the joke? Is that hidden in the "that d²y/dx² is negative between x=26 and x=29" bit which I specifically don't follow?
I hope by now you understand, thanks to other people's explanations, what "d²y/dx² is negative" means. The joke is, as you surmise, in taking Smallfurry's vague first proposition (26 and 29 are different but equal) as a complete statement of something which has been mathematically proven, and then using questionable mathematics to "prove" that his second proposition (27.5 can be no better than 26 or 29) must be wrong.
I hope by now you understand, thanks to other people's explanations, what "d²y/dx² is negative" means. The joke is, as you surmise, in taking Smallfurry's vague first proposition (26 and 29 are different but equal) as a complete statement of something which has been mathematically proven, and then using questionable mathematics to "prove" that his second proposition (27.5 can be no better than 26 or 29) must be wrong.