求函数f(x,y)=xyln(x^2,y^2)的极大值点,答案为(1/√2e,-1/√2e),

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求函数f(x,y)=xyln(x^2,y^2)的极大值点,答案为(1/√2e,-1/√2e),
求函数f(x,y)=xyln(x^2,y^2)的极大值点,答案为(1/√2e,-1/√2e),

求函数f(x,y)=xyln(x^2,y^2)的极大值点,答案为(1/√2e,-1/√2e),
f(x,y)=xyln(x^2+y^2) (中间是+吗)
所以
fx(x,y)=yln(x^2+y^2) +2x^2y/(x^2+y^2)=0 （*）
fy(x,y)=xln(x^2+y^2) +2xy^2/(x^2+y^2)=0
移项,相除得
y/x=x/y
x=y或x=-y
1.x=y代入（*）得
yln2y^2=-y
ln2y^2=-1,2y^2=1/e,y^2=1/2e
x=y=1/√2e,或-1/√2e
2.x=-y代入（*）得
yln2y^2=-y
ln2y^2=-1,2y^2=1/e,y^2=1/2e
x=-y=1/√2e,或-1/√2e
下面继续求二阶偏导数再判断,可得结论!自己做吧!

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