PokeVideoPlayer v23.9-app.js-020924_
0143ab93_videojs8_1563605 licensed under gpl3-or-later
Views : 804
Genre: Education
License: Standard YouTube License
Uploaded At Aug 14, 2023 ^^
warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
Rating : 5 (0/36 LTDR)
100.00% of the users lieked the video!!
0.00% of the users dislieked the video!!
User score: 100.00- Masterpiece Video
RYD date created : 2024-06-04T16:22:13.540589Z
See in json
@MichaelRothwell1
1 year ago
This is a beautifully simple solution to this constrained optimization problem.
However, I think we need to show that the limit of 6 can actually be achieved, which of course it can, with (x, y)=(3, 3) [and the lower limit can be achieved with (x, y)=(-3, -3)].
This problem can also be understood visually, by considering the family of lines of the form x+y=k, where we want to find the largest k such that x+y=k intersects the constraint curve x²+y²=18. Naturally, the extreme values of k will occur when x+y=k just touches, i.e. is tangential to, x²+y²=18. Although this can be solved using calculus, it can also be seen by symmetry that this occurs when x=y, so when (x, y)=(3, 3), which gives the maximum and when (x, y)=(-3, - 3), which gives the minimum.
A general method for solving this kind of problem is to use Lagrange multipliers.
|