What part of speech is "best" in the sentence, "It is best to make an appointment early in the day."

Unless "best" is followed by a noun which it is modifying, the word is being used as an adverb.

http://www.answers.com/best
You can see here -- and in any dictionary -- that they are telling you the part of speech for the word. In this case, they indicate that it can be either an adjective or an adverb. So ... if there's no noun right after it to be modified,* it is serving as an adverb.

=)

*An example of such a sentence would be this: She is wearing her best coat tonight. ("Best" is the superlative of "good" and it's modifying "coat.")