Practical:Finding local extrema
This article provides a summary of the many approaches that can be used to find the points of local extremum for a function. The goal of the article is to describe procedures that can be used to simultaneously compute all the points of local extremum as well as points of one-sided local extremum. This includes points of local maximum, points of local minimum, and domain endpoints that are points of one-sided local maximum or minimum.
We assume for simplicity that the domain of the function is an interval or union of finitely many intervals each of which may be open, closed, or half-open half-closed.
Non-calculus versus calculus approaches
This article focuses mainly on calculus approaches to finding local extrema, so prior to beginning it, we will briefly describe the key distinction between non-calculus and calculus approaches.
Non-calculus approaches are approaches that do not involve computing the derivative of the function, but use direct comparisons of function values between points. A typical example of a non-calculus approach is the observation that attains a local minimum at because the square of any nonzero number is positive.