I could feign that there was no world, I could not feign that I did not exist. (chapter 4, paragraph 3; Discourse on Method) Based on this context, the word feign most likely means: deny, argue, pretend, believe

compare & contrast informative essay/speech

when speaking or writing for the sole purpose of providing information in order to give audience members a good basis for making a decision, you would present an informative speech or essay.   because you wouldn’t want to be persuading the audience by arguing for one type of exercise over the other, you wouldn’t choose a persuasive/argumentative technique.   to fairly, and without bias, present information about the pros and cons of each type exercise, a compare/contrast, informative speech/essay would be the best bet.