적극적이다 = is outgoing and aggressive in attitude. (used of a person, organization).
활동적이다 = lively and energetic with a lot of movement. (of a person).
활발하다 = active and lively (of activities, events; or of a person).
So 활동적이다 is antonym of listless or sedentary.
활발하다 is antonym of depressed or subdued.
적극적이다 is antonym of shy or reserved.