Here's why:
* Adverbs modify verbs, adjectives, or other adverbs. They tell us how, when, where, or to what extent something happens.
* "Dutifully" describes the manner in which something is done.
For example:
* "The dog dutifully obeyed its master." ("Dutifully" modifies the verb "obeyed".)
* "She completed her work dutifully." ("Dutifully" modifies the verb "completed".)