I am teaching an introductory calculus course for high school juniors and seniors. It is not formally described as an AP Calculus course, but it is supposed to map roughly onto Calculus AB.
The students needed more review of algebra, trigonometry, and precalculus than one might hope, and as a result, we are quite far behind, and risk not getting to integrals and the fundamental theorem of calculus, which are supposed to be the high point of this course. So I am looking for things to cut along the way.
The most obvious candidate seems to be Newton's method. There is a section on it before the section on antiderivatives. It seems to be something of a side note.
Am I going to regret cutting this? Does it serve some pedagogical purpose for introducing anti-derivatives or integrals? Is there something else that's going to depend on this method when they get to Calculus II?