Academic Journal of Mathematical Sciences, 2024, 5(3); doi: 10.25236/AJMS.2024.050302.
Qin Ruonan, Yang Kaifan
School of Mathematics and Computer Science, Shaanxi University of Science and Technology, Hanzhong, Shaanxi, China
With the reform of secondary school mathematics, teaching gradually emphasizes tracing the nature of the problem. Conditional extreme value is one of the knowledge points that bridges higher mathematics and elementary mathematics. This paper adheres to the idea of the high point of view, connects the conditional extreme value in higher mathematics with the most value problem taught in secondary school, and uses Lagrange number multiplication to solve the distance, area extreme value problem. Conic curve as an example, the high point of view of the background of the conditional extreme value solution and high school commonly used to solve the inequality problem ideas. By solving the partial derivatives listed in the system of equations to determine the coordinates of the point, the practice is simple, novel ideas, easy to operate. It is conducive to students' expansion of ideas and enhancement of disciplinary literacy.
high point of view; conditional extremes; conic curves
Qin Ruonan, Yang Kaifan. Application of Conditional Extreme Values in Higher Perspective—Take "Conic Curve" Problems as Examples. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 3: 8-15. https://doi.org/10.25236/AJMS.2024.050302.
[1] HU Lin,ZHAO Silin. Analysis of high school mathematics test questions under high viewpoint[J]. Middle School Mathematics, 2019, 13:36-37+39.
[2] Department of Mathematics, East China Normal University. Mathematical analysis [M]. Beijing: Higher Education Press, 2010.
[3] Ministry of Education of the People's Republic of China, ed. General high school mathematics curriculum standard 2017 edition revised in 2020[M]. Beijing: People's Education Publishing House, 2020
[4] Wang, Donghai. A multi-perspective investigation on the solution of a binary function maximum value problem [J]. Research on Secondary Mathematics, 2024(03):48-50.
[5] Yu Tieqing. Research on multivariate maximization problems in high school mathematics based on conditional extremes [J]. Research on Secondary School Mathematics (South China Normal University Edition), 2020,(14):37-38.
[6] Peng Haiyan, Li Wei. Highlighting graphical investigation and strengthening algebraic reasoning--an analysis of the solution to the topic of "plane analytic geometry" in the 2022 college entrance examination [J]. China Mathematics Education, 2022, (Z4):78-85.
[7] Li Hongdai. Mathematical ideas for solving the problem of centrality of conic curves[J]. Secondary school teaching reference, 2023,(29):22-25.
[8] Gao Binbo. An investigation of the area problem of triangles in analytic geometry[J]. Mathematics and Science World (High School Edition), 2022(24):14-15.
[9] Chen Xiaolu. An investigation of the solution and error points of a conic section area problem[J]. Research on Secondary School Mathematics, 2024,(03):27-29.
[10] Zhou Mali, Zhang Jinsong. Implications of mathematical ideas of high viewpoints for secondary school mathematics teaching [J]. Secondary Mathematics Monthly, 2014,(03):7-10.