好吧问答库 > 求函数y=2x눀+3⼀x(x>0)的最小值

求函数y=2x눀+3⼀x(x>0)的最小值

2025年04月05日 05:36
有4个网友回答
网友（1）：

此题应用基本不等式推广，构造积为定值

y=2x²+3/x                  （把3/x拆成3/2x+3/2x）

y=2x²+3/2x+3/2x

≥3  ³√(2x²·3/2x·3/2x)   当且仅当2x²=3/2x时，取等号，此时x=³√3/4

最小值是3/2  ³√12

网友（2）：

y=2x²+3/x
y=2x²+3/2x+3/2x
≥3 ³√(2x²·3/2x·3/2x)
=3 ³√(3/2)
=3/2 ³√12
最小值是3/2 ³√12

网友（3）：

x = sqrt(sqrt(3/4))时，y = sqrt(3) + 3/sqrt(sqrt(3/4))

网友（4）：

求导
4x-3(x^(-2))= 0
x=(3/4)的立方根
代入求最小值

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