设f(x,y)与
均为可微函数，且
，已知(x0，y0)是f(x,y)在约束条件
下的一个极值点，下列选项正确的是
(A) 若f′x(x0，y0)=0，则 f′y(x0，y0)=0．
(B) 若f′x(x0，y0)=0，则f′y(x0，y0)≠0．
(C) 若f′x(x0，y0)≠0，则f′y(x0，y0)=0．
(D) 若f′x(x0，y0)≠0，则f′y(x0，y0)≠0．
参考答案：D
解析： 利用拉格朗日函数
在(x0，y0，λ0)(λ0是对应x0，y0的参数λ的值)取到极值的必要条件即可．
作拉格朗日函数F(x，y，λ)=f(x，y)+f(x，y)，并记对应x0，y0的参数λ的值为λ0，则
消去λ0，得
，
整理得
.因为
)，
若f′x(x0，y0)≠0，则f′y(x0，y0)≠0．故选(D)．
[评注] 本题考查了二元函数极值的必要条件和拉格朗日乘数法．
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