YLL討論網

#ed_op#P#ed_cl#

GFIF 寫到:電腦中有一份文件，需要有24平方單位的列印面積，#ed_op#BR#ed_cl#列印紙上下各要有1.5單位、左右各要有1單位的保留空間，#ed_op#BR#ed_cl#請問這張列印紙最少要有多少平方單位？

#ed_op#/P#ed_cl##ed_op#P#ed_cl#設長ａ，寬ｂ#ed_op#/P#ed_cl##ed_op#P#ed_cl#所以AB=24#ed_op#/P#ed_cl##ed_op#P#ed_cl#求ｍｉｎ（ａ＋２）（ｂ＋３）#ed_op#/P#ed_cl##ed_op#P#ed_cl#即求ｍｉｎ（３ａ＋２ｂ）#ed_op#/P#ed_cl##ed_op#P#ed_cl#由算幾不等式可知，ａ＝４，ｂ＝６，有ｍｉｎ值５４#ed_op#/P#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

#ed_op#DIV#ed_cl#設 "列印面積" 為 x * y (x 為寬, y 為高).#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#x * y = 24  #ed_op#BR#ed_cl#y = 24 / x .... (1)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以紙張面積就是 (x + 2)(y + 3), #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#y 用 (1) 式代入後, 為 (x + 2)(24/x + 3) #ed_op#BR#ed_cl#= 3·x + 48/x + 30 .... (2) ← 找它的最小值.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我是個懶人, 用微分. 令 (2) 式的微分 = 0, 來找原式斜率為 0 的 x .#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#微分後:  #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#3 - 48/x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# = 0 #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#3x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# - 48 = 0 (上式 = 兩邊同 * x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#)#ed_op#BR#ed_cl#3(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# - 16) = 0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以 x = 4 ( -4 不管) 有極值, #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#x=4 代回 (2) 式#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#3·4 + 48/4 + 30 = 54#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

電腦中有一份文件，需要有24平方單位的列印面積，
列印紙上下各要有1.5單位、左右各要有1單位的保留空間，
請問這張列印紙最少要有多少平方單位？