This problem is extremely easy.
ごくごく普通の一日だった。
It was a very ordinary day.
This is an utterly ordinary family.
Only an extremely small number of people agreed with that idea.
Such a thing happens only extremely rarely.
極めて is a literary, formal intensifier used in writing and speeches, while ごくごく is more conversational.
至って is a somewhat formal way to say 'extremely' often used with calm or ordinary states, while ごくごく is more casual and emphatic.
とても is the everyday, generic word for 'very', whereas ごくごく specifically emphasizes an extreme degree in a more colloquial register.
Rare kanji spelling; the kana form is strongly preferred.
Rare kanji spelling; the kana form is strongly preferred.
Reduplication of ごく (極), an adverb meaning 'very' or 'extremely', for emphasis.