What effect is achieved when using the gerundive form versus the infinitive form in this sentence?

Solution 1:

[1] Try [getting some rest].

[2] Try [to get some rest].

There is a difference in meaning.

[1] means "test the effectiveness of", while [2] means "endeavour".

Both clauses are functioning as complement of "try".

Solution 2:

I would say it was the other way round!

The infinitive (the latter) means 'Attempt to do it'. You might advise someone recovering from an illness to try to get some rest because it would help them.

The gerund[ive] functions like a noun. As your textbook says, 'getting some rest' is suggested as a possible solution to a problem (such as not being able to think clearly).

Neither is 'more correct' than the other, but there is this slight difference in meaning.