Meaning of justify

A computation, properly laid out, is of course a proof. However, many students, after years of multiple choice tests, have learned to take the point of view that the answer is the only thing that matters.

"Justify" can be a reminder that the problem will be graded carefully, that (contrary to their usual experience) a slapdash computation will not necessarily get full marks.

I do not think that "justify" carries any connotation of "you need only show necessity but not sufficiency."

"Prove," in a course context, can often mean that a more or less specific set of tools should be used. "Justify" has a more informal feel, but I do not think of it as carrying a lower level of precision.

To me, "justify" means to lay out the mathematical thought process step by step, so that the line from the starting point to the ending point is connected.

It is a bit less formal than a proof, which has certain logical requirements, but it means, "show enough work so that I know that you get the whole thing."