eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2022-05-18 10 1 12 14 10.12691/tjant-10-1-3 TJANT20221013 article Guoqiang Dang dang@mail.bnu.edu.cn 1 School of Mathematical Sciences, Beijing Normal University, Beijing, P.R. China This research is focusing on the extremum of a given function which involves triangle functions. We collect some typical examples from ordinary high school mathematics teaching and demonstrate several typical mistakes which were usually posed by ordinary high school students usually and analyze the reasons for the errors. These results will be used to help ordinary high school students to well understand AM-GM inequalities and related applications for maximum and minimum values of triangle type functions. http://pubs.sciepub.com/tjant/10/1/3/tjant-10-1-3.pdf AM-GM inequalities error analysis extremum values