In which sentence is the quoted word used correctly?

The sentence "Affecting radical changes" uses the word correctly because "affecting" is a verb form that means to have an impact on something, which fits well in this context. The word "affect" can be used to describe the action of causing a change or influence in something, making it the appropriate choice when discussing the consequences or influence of significant changes.

In contrast, the other options misuse either the form of the word or the applicable context. For instance, "insight" in the first two options should actually be "incite" and "insight," which refer to understanding and inspiration, respectively, rather than stimulating action or providing deep perception. "Affect" is often confused with "effect," and in the third option, "affect" should be replaced with "effect" to convey the correct meaning of producing a result. Hence, "affecting radical changes" correctly captures the intended meaning of influencing changes.