Database functional dependency candidate keys

A superkey (and therefore a candidate key) that does not contain all attributes must contain at least an attribute set that is the left side of a functional dependency. Otherwise it would not be possible to generate an additional attribute from the attribute set of this superkey and this contradicts the definition of a superkey.

But a subset of ABCDE containing at least one of C,AB,AE or DE is already a superkey and to be minimal it is necessary that it contains only one of these subsets.

So the only subsets that must me investigated are that that are supersets of AC. But a superset of AC cannot be a minimal superkey because C already is a key.

Therefore the only candidate keys are C,AB,AE and DE

You can't tell the functional dependencies just from the schema.

If you knew that the schema was in third normal form (3NF) or higher and you knew that there are no other candidate keys other than the primary key, then you would know that every non-key attribute was fully functionally dependent on the primary key.

Except for this particular situation, there is nothing about a schema that conveys functional dependency. The purpose of a schema is to convey table structure, not functional dependencies.