The word interrogate is usually pronounced something like in-TEH-ruh-gayte.
But we pronounce the grammatical structure (or at least, I learnt to pronounce it) 'interrogative' as in-tuh-RAU-guh-tive. Excusing my probably inconsistent renderings of the pronunciations, what explains this difference, and why is there such a difference in stress?
It's an exception, more or less. (The usual "rule" given for "-ative" words is indeed to keep the stress in the same place as the verb: see my answer to Is there a rule for the position of the accent (stressed sound) in words ending with -ative?). As John Lawler said in a comment, stress shift upon affixation can be seen in many English words, but it's not always predictable. (For example, the stress in the word ˈrĕlative is earlier than the stress in the word reˈlāte, but the stress in the word creˈātive is in the same place as the stress in the word creˈāte).
In polysyllabic words from Latin, stress often falls on the third-to-last ("antepenultimate") syllable, unless the second-to-last syllable has a long vowel (as in the word corˈrōsive) or ends in a consonant (as in the word colˈlĕc.tive; but note that there are a few exceptional words like ˈădjec.tive where the second-to-last syllable ends in a consonant but is not stressed.) But there are a number of cases where stress falls earlier than the third-to-last syllable, often due to influence from the position of the stress in a related word, and most polysyllabic -ative adjectives fall into this category: we don't see a stress shift relative to the verb in words like coˈŏperative, iˈmăginative, ˈspĕculative, ˈdĕcorative, etc.
There are at least a few other -ative words that show the same stress shift as interrogative. The ones that I know of are inˈdĭcative, corˈrĕlative, and deˈrŏgative (vs ˈindicate, ˈcorrelate, ˈdĕrogate).
I disagree with John Lawler's statement that the last syllable in interrogative is stressed. For me, the "t" before the final "i" can be lenited to a voiced flap, something that typically cannot occur at the start of a stressed syllable. I believe it is possible for the last syllable to be stressed in certain accents, but it is not necessarily stressed in all accents. See the following question and its answers for more discussion of this issue: Why isn't the T in “relative” flapped?
