※ 引述《loseaguy (L)》之銘言:
: A box with an open top is to be constructed by cutting x inch by x inch
: squares from the corners of a 42 inch by 32 inch piece of cardboard. What
: should the dimensions be, to two decimal places, that would maximize the
: volume.
: 可以幫忙解釋這題嗎?不僅題目看不太懂,也不知從何算起....XD 謝謝!!
一個邊長是 42*32 的平板,要在這個平板的四個角落都割下一個 x*x 的正方形,
這樣就可以把四個邊折起來,變成一個box with an open top.
欲求能使此box有最大容積的x。
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解:
容積 = (42-2x)*(32-2x)*x
欲求極值,令微分後=0然後解出 x = 18.6 or 6
18.6不合(因為32-2x為負),故解 = 6.
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02/11 13:13, , 1F
02/11 13:13, 1F
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