Hi,
I would like to share with you the way I was taught to test a purpose clause to determine whether it is adverbial or adjectival (relative).Here it is for you to review to see if that teaching is off base:
If we look at a noun in the main clause and can insert a relative pronoun right after it to show that the pronoun can become the subject of the verb in the purpose clause, the purpose clause is adjectival. If we cannot, it is adverbial. For example:
adjectival:
I need a nurse to care for my mom.
It is the nurse who can care for my mom - not I; therefore, to care for my mom is adjectival. As we can see, that sentence can be rewritten as follows:
I need a nurse who can care for my mom.
adverbial:
The soldiers took back some land to build the school.
Now, since the land cannot build the school, to build the school is definitely adverbial. In fact, the sentence can be rewritten without changing its meaning as follows:
The soldiers took back some land so that they could build the school.
So back to Taka’s statement, “I need some way to stop my headache.” Is 'to stop my headache’ adverbial or adjectival? To answer that, we need to determine whether I or some way stops the headache.
Evidently, it is not I who stops the headache else I would not need a way. Therefore, in this case the subject of stop is the omitted relative pronoun that that stands for some way. Hence, ‘to stop my headache’ is adjectival.