Max. & Min
2015-06-16 7:43 pm
6 sq. meters of tin plate is used to make a square based container(no lid). Let base length = a and height = b. Find the value of a and b such that the volume of the container is a maximum. (Ans correct to 3 sig. fig.)
回答 (2)
2015-06-16 8:06 pm
✔ 最佳答案
Please check:http://i.imgur.com/vIs6tGm.jpg
2015-06-16 12:09:55 補充：
註：由於原問題設置代數後面並無單位，因此本人假設 a、b 均包含其單位 m，最終數值亦包括其單位。
2015-06-16 8:19 pm
volume V = a²b ...... [1]
surface area :
a² + 4ab = 6
4ab = 6 ‒ a²
b = (6 ‒ a²)/4a ...... [2]
Put [2] into [1] :
V = a²(6 ‒ a²)/4a
V = (6a ‒ a³)/4
dV/da = (6 ‒ 3a²)/4
dV/da = 3(2 ‒ a²)/4
d²V/da² = ‒6a/4
d²V/da² = ‒3a/2
2015-06-16 12:19:13 補充：
When a = √2 :
dV/da = 0
d²V/da² = ‒3(√2)/2 < 0
Hence, when V is the max :
a = √2
a = 1.41 (m)
b = (6 ‒ 2)/4√2
b = (√2)/2
b = 0.707 (m)
surface area :
a² + 4ab = 6
4ab = 6 ‒ a²
b = (6 ‒ a²)/4a ...... [2]
Put [2] into [1] :
V = a²(6 ‒ a²)/4a
V = (6a ‒ a³)/4
dV/da = (6 ‒ 3a²)/4
dV/da = 3(2 ‒ a²)/4
d²V/da² = ‒6a/4
d²V/da² = ‒3a/2
2015-06-16 12:19:13 補充：
When a = √2 :
dV/da = 0
d²V/da² = ‒3(√2)/2 < 0
Hence, when V is the max :
a = √2
a = 1.41 (m)
b = (6 ‒ 2)/4√2
b = (√2)/2
b = 0.707 (m)
收錄日期: 2021-04-16 16:51:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150616000051KK00045