[sidlls]

Back when I was in high school Newton's Method was typically introduced as a method to find roots of a polynomial, usually in "Algebra 2" or Trigonometry or about then. That's because there is an easy to grasp formula for it that can be used in the context of a very familiar mathematical construct (polynomials) and produced from differentiation that doesn't technically require an understanding of calc to use (as opposed to actually understand, derive, etc.). I still use it pre-calc when I tutor younger students because it's a great exploratory tool.