A wire of length 100cm is cut into at most two pieces.
Each piece is bent into the shape of a square.
How should this be done to minimize the sum of the area(s) of the square(s)?
To maximize it?
calculus---optimization
2013-10-16 7:09 am
回答 (2)
2013-10-16 10:23 am
✔ 最佳答案
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參考: pingshek
2013-10-16 7:31 am
The 2 pieces of wire are x cm and (100-x) cm
Area = (x/4)^2 + [(100-x)/4]^2
= x²/16 + (1/16)(10000-200x+x²)
= x²/8 + 625 - (25/2)x
dA/dx = x/4 - 25/2
d²A/dx² = 1/16 > 0 ==> min
when dA/dx = 0 ==> x/4 - 25/2 = 0 ==> x = 50 cm
To maximize it
Cut the wire into 2 pieces with length 100 cm + 0 cm
Area = (x/4)^2 + [(100-x)/4]^2
= x²/16 + (1/16)(10000-200x+x²)
= x²/8 + 625 - (25/2)x
dA/dx = x/4 - 25/2
d²A/dx² = 1/16 > 0 ==> min
when dA/dx = 0 ==> x/4 - 25/2 = 0 ==> x = 50 cm
To maximize it
Cut the wire into 2 pieces with length 100 cm + 0 cm
收錄日期: 2021-04-27 20:36:27
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