Yahoo Answers: Answers and Comments for Pure Maths Question [語言]
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From Anonymous
enUS
Thu, 01 Nov 2012 06:21:49 +0000
3
Yahoo Answers: Answers and Comments for Pure Maths Question [語言]
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https://answers.yahoo.com/question/index?qid=20121101000016KK00788
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From Joyce: 你們可以用Derivative Method解答嗎？
https://answers.yahoo.com/question/index?qid=20121101000016KK00788
https://answers.yahoo.com/question/index?qid=20121101000016KK00788
Thu, 01 Nov 2012 13:52:50 +0000
你們可以用Derivative Method解答嗎？

From DaSaGwa: Terry +1! Nice job! you didn't use "...
https://answers.yahoo.com/question/index?qid=20121101000016KK00788
https://answers.yahoo.com/question/index?qid=20121101000016KK00788
Thu, 01 Nov 2012 07:41:49 +0000
Terry +1! Nice job! you didn't use "derivative" but "completing the square" (algebraic method).
20121101 07:47:19 補充：
calculus method:
assume x and y are the two side of the rectangular, hence
2x + 2y = A (A is fixed perimeter)
==> x = 1/2(A 2y)
20121101 07:50:30 補充：
area of rectangular = xy = 1/2(A2y)y = Ay/2 y^2
for area to be the maximum, d(area)/dy = 0
hence, A/2 − 2y = 0 ==> y = A/4, so x=y=A/4, a square !
20121103 08:55:51 補充：
Using what method to solve a problem depends upon the level of schooling. If a person can understand the meaning of derivatives, then why not uses a more advance way to solve a problem.
20121103 08:57:34 補充：
However, I feel, no matter what level of schooling you are in, a person shall always know a lower level method. After all, it is a foundation for more advanced method.

From Terry: 假設矩形的周長是 A, 令此矩形的其中一邊長是X,則另一邊長必為(A/2X)
矩形的面積...
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https://answers.yahoo.com/question/index?qid=20121101000016KK00788
Thu, 01 Nov 2012 07:28:59 +0000
假設矩形的周長是 A, 令此矩形的其中一邊長是X,則另一邊長必為(A/2X)
矩形的面積則為:X*(A/2X)=X*A/2X^2
利用"配方法"則上式可寫成(X^2AX/2+(A/4)^2)+0.5A^2=(XA/4)^2+A^2/16
當X=A/4的時候,可以得到最大面積=A^2/16
此時矩形的形狀即為正方形(因為邊長都是A/4)