函数u=sinxsinysinz满足条件x+y+z=π/2(x>0,y>0,z>

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问题 函数u=sinxsinysinz满足条件x+y+z=π/2(x>0,y>0,z>0)的条件极值为(  )。A.1B.0C.1/6D.1/8

选项 A.1
B.0
C.1/6
D.1/8

答案 D

解析 构造函数F(x,y,z)=sinxsinysinz+λ[x+y+z-(π/2)],则解得x=y=z=π/6把x=y=z=π/6代入u=sinxsinysinz得u=1/8。
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