Most references do not use or avoid using terms when discussing critical points that are not maximum or minimum. But for the sake of asking a general term that encompasses critical points which are not maximum or minimum, what would be the term? I see terms like saddle point and point of inflection in some cases but I know that those terms have their own meaning and might not be restricted to the definition "a critical point not maximum or minimum". I just really want to use a formal term and not keep on stating that it is not an extreme point.
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I've not heard of one. You can always choose your own good terminology, and define it clearly. For instance "nonextreme critical point" seems quite clear to me. – Lee Mosher May 17 '22 at 12:53