I'm certain that when I was in secondary school most of my classmates would be able to answer (b) and (c) of that question since it's a standard 'set derivative

I'm certain that when I was in secondary school most of my classmates would be able to answer (b) and (c) of that question since it's a standard 'set derivative equal to zero' question. Part (a) is indeed vague, and they want you to prove something that's incorrect, but it's not hard to see what they want to hear. Ugh, that brings back memories of answering vague questions in such a way that you know will make the teacher happy, but is actually incorrect. I remember one instance where a question on a physics exam asked us to solve a problem that did not have an unique answer (it boiled down to 3 variables and only 2 equations). So I wrote as my answer an explanation why the question could not be solved, which the teacher gave 0 points for. Later in the exam review in class I asked him what the correct answer was, and he gave incorrect reasoning. After I politely pointed out that his answer was incorrect I got 15 minutes of "public shaming" in class about how stupid I was and how dare I disagree with him. Afterwards I sent that question to a physics professor in a university, who also said that the question could not be solved. I sent that to my teacher which only made him more angry. Luckily those days are over.