Identify the phrasal category of the bold constituent "extremely dedicated" in the following sentence. You have an extremely dedicated team.

You have an extremely dedicated team.

The words "extremely dedicated" constitute an adverbial adjective phrase that is a pre-modifier to the head noun "team." The phrasal constituents "extremely dedicated" are pre-modifiers of the noun phrase "an extremely dedicated team," with "team" being the head noun of the phrase. 
The word "extremely" is an adverb, while "dedicated" is an adjective, "dedicated" being the adjectival past participle form of the verb "dedicate." Both the adverb and the adjective fill the pre-modifier slot adjacent to the head noun. The simple description of the order of pre-modifiers in a noun phrase is this:
Article, possessive + quantifying determiner + definitive, pronoun, article determiner + numerical determiner + adverb, adjective participle (phrase) + noun modifier (phrase) + head noun. [An even simpler description is available from the British Council and a more complex one from BYU.]
Noun phrase construction can be constituted of one single noun or pronoun, as in "[You] Go home." Noun phrases can also be complex having many pre-modifying quantifiers, determiners, adjective and adverbial adjective or noun phrases, as in this elaborate example: "Only half of the twenty-seven diversely smallish brightly decorated Easter eggs were found." The italicized words are pre-modifying quantifiers and determines, adverbs and adjectives. "Easter eggs" is the countable compound head noun.
The final constituent modifying phrase of the "Easter egg" example matches the targeted constituents in your sentence. Specifically, "brightly decorated" is an adverbial adjective phrase pre-modifying a head noun just as "extremely dedicated" is an adverbial adjective phrase pre-modifying a head noun.
http://learnenglish.britishcouncil.org/english-grammar-reference/noun-phrases