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

Question

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

Answer 1

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/yx=y或x=-y1.x=y代入（*）得yln2y^2=-yln2y^2=-1,2y^2=1/e,y^2=1/2e...