Relative clauses: "I did the best I could."
I did the best I could.
The sentence above can be rephrased:
- I did the best that I could.
In these two examples (that) I could is a relative clause. However, I am not sure whether it is modifying best or the best or an ellipted element. What exactly is this clause modifying?
Secondly, what type of phrase is the best here and what type of word is best?
This doesn't answer OP's question, but it addresses the confusion another answerer here has.
He said in his answer "best is a noun in I did the best I could, but an adjective in I did the best thing I could".
I strongly oppose that conclusion. In my opinion best is an adjective both in I did the best I could and in I did the best thing I could.
Here are the reasons -
- A noun can't be modified by an adverb (A noun phrase can, but we are talking about only noun not the noun phrase). An adjective, however, can be pre-modified by an adverb like very.
This time they cared enough to serve the very poor.
See in the sentence above poor, though, seems like a noun. But it's actually not. How poor? very. The adverb very pre-modifies an adjective. So poor is not a noun.
She is the most beautiful of them.
Here beautiful is not a noun. most beautiful is the superlative form of the adjective beautiful.
Similarly, in OP's quoted sentence best is an adjective.
ANSWER TO OP -
I did the best (that) I could (do).
The mention of do here is optional. Similarly optional is the mention of relativizer in the relative construction - (that) I could (do).
The antecedent here is the noun phrase (NP) - the best.
Now it's a different type of noun phrase where the head of the noun phrase is fused with its internal modifiers. Such NPs are called Fused-head NP.
I did [the best] [(that) I could (do) ___].
A few omissions in the sentence:
I did the best (thing or things) (that) I could (do).
"Thing" is omitted because it is not necessary. The noun best itself can mean "the best thing". Therefore, we could say the relative clause is modifying its antecedent the best.
If you don't omit the noun thing (s), "best" will be the superlative form of the adjective good. Otherwise, "the best" is a noun phrase functioning both as an object of the transitive verb to do and an antecedent of the relative clause.