To answer this question, we need to understand the meaning of each option and choose the one that best fits the context of the sentence.
Option A) mortifying - This option means causing embarrassment or humiliation. In the context of the sentence, it doesn't make sense to say that the older child had a reputation for causing embarrassment or humiliation in high school, but then calmed down in college.
Option B) appeasing - This option means pacifying or satisfying someone. In the context of the sentence, it doesn't make sense to say that the older child had a reputation for pacifying or satisfying trouble in high school, but then calmed down in college.
Option C) curtailing - This option means reducing or limiting. In the context of the sentence, it doesn't make sense to say that the older child had a reputation for reducing or limiting trouble in high school, but then calmed down in college.
Option D) instigating - This option means provoking or initiating something, usually negative or problematic. In the context of the sentence, it makes sense to say that the older child had a reputation for provoking or initiating trouble in high school, but then calmed down in college.
Therefore, the correct answer is D) instigating. This option is correct because it accurately describes the older child's reputation for causing trouble in high school.