作者FoggyCloud (雲霧)
看板Math
標題[微積] 最少的材料做成的罐頭
時間Tue Jul 26 22:56:35 2011
A closest cylindrical can is to hold 500cm^3 of liquid ,
how should we choose the height and radius to minimize the amount of
material needed to manufacture the can?
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1F：推 ntust661 :目標函數 07/26 22:57
2F：→ ntust661 :pi*r^2*h = 500 07/26 22:57
3F：→ ntust661 :f(A) = 2*pi*r^2 + 2*pi*r*h 07/26 22:58
4F：→ ntust661 :h = 500/pi/r^2 07/26 22:59
5F：→ ntust661 :代入 f(A) 07/26 22:59
6F：→ ntust661 :f(A) 就會變成 f(r) 07/26 22:59
7F：→ ntust661 :若表面積要最小，至少一階導數要等於零 07/26 22:59
8F：→ ntust661 :f'(r) = 0 , find r 07/26 23:00
9F：→ ntust661 :then calculate h 07/26 23:00
10F：→ FoggyCloud :thanks! 07/26 23:19
11F：推 young11539 :CHECK f''(r)>0 07/27 01:34