I have an argument like that in my calculus 1 class in college, it was an optimization problem but the professor never said that the optimization variable was a constant, so you couldn’t differentiate it to zero and do the normal process that you typically do. So I just wrote that given that the perimeter wasn’t a constant the area to optimize goes to infinite Givin x -> inf; y -> 0, without loss of generality. He marked me zero we discussed about it and I said that I don’t care because I’m going to get a 10 next test if he didn’t fucked up the question. At the next exam I made some stupid error but he still gave 9/10 for the overall class because he came to accept that he wrote the question wrong and I was the only in the class actually caring and giving the class some dedication.