Recalcitrant" comes from the Latin word "recalcitrare," which means "to be disobedient." The word "recalcitrant" means "stubbornly resistant." Two synonyms are "obstreperous" and "willful." Two antonyms are "compliant" and "obedient."
You need an adverb here, as it will modify the verb, not a noun (or is not a predicate) so the correct answer is "well" - option b.
