【京大2011】空間図形と最大値・最小値【方程式・値域】

⭐️ "Oshie Math" allows you to ask Hayashi unlimited questions for a fixed monthly fee. You can try asking questions for free once! https://oshiemath.com/ ⭐️ "Hayashi Math Class," a specialized mathematics school where you can receive direct instruction from Hayashi. Please come for a trial lesson and interview! https://hayashi-math.com/ ✅ Official LINE for students applying to top universities: https://lin.ee/lI7n1SJ Subscriber benefits & live streams for applicants ℹ️ Shunsuke Hayashi's profile https://hayashishunsuke.com/profile/ ・Graduated from Sakae Higashi Junior High School → Chikuma High School → University of Tokyo, Faculty of Science, Department of Physics ・Scored 90% on the second-stage mathematics exam at the University of Tokyo, passing the exam as a current student ・2014 Japan Physics Olympiad Gold Medal ・Placed first place in the 2014 University of Tokyo Physics Mock Exam ℹ️ Please note ・The explanations are Shunsuke Hayashi's own and are not official university information. ・Amazon Associates links will be used when introducing books, etc. ★Correction: The correct coefficient for sinθ at 29:57 is 1/√3 in all cases! This problem concerns the maximum and minimum values ​​of functions in space, from the 2011 Kyoto University Science Mathematics exam. Consider the points (x, y, z) on the intersection of the sphere S centered at the origin and the plane α, and find the maximum and minimum values ​​of x, y, and z. The video covers two solution methods. The first method (which focuses on the solution to the cubic equation) is the standard. It is something that all applicants to prestigious universities should be able to do. The second solution method uses vectors to parametrically express the coordinates of the points on the intersection (above). Many people will find this novel, but what is being done is surprisingly simple, and I personally prefer this solution method. If you're interested, please study the latter as well. ---------- Table of Contents 00:00 2011 Kyoto University Science Mathematics [5] 00:49 Two Solutions 01:05 Solution 1: Existence of a Common Point 05:05 Solution 1: Conditions Satisfied by p (= xyz) 06:28 Solution 1: Rewriting the Condition 11:49 Solution 1: f(t) = p Has 3 Real Solutions 18:31 Summary of Solution 1 21:04 Solution 2: Using Space Vectors 23:14 Solution 2: Two Unit Vectors 25:12 Solution 2: Finding the Coordinates of a Point on a Circle 30:05 Solution 2: Viewing xyz as a Function of cosθ 32:16 Solution 2: Min and Max of the Function g(α) 33:34 Summary of Solution 2 34:58 Supplement: Range of α 36:39 Comments on the two solution methods 37:35 Advice for learners 38:19 Conclusion