how to know when to use binary search on answer

Ask two things:
1. If I guess an answer X, can I check if X works in O(n)?
2. If X works, does every bigger X also work (or every smaller)?

If both yes, binary search over X.

Usually the question says something like "minimum possible maximum" or "smallest X such that".

Practise: koko, ship packages, split array largest sum, aggressive cows, book allocation.