求Z=x^3-y^3-3xy的极值和极值点答:Z=f(x,y)=x^3-y^3-3xy 分别对x,y求偏导:fx=3x^2-3y fy=-3y^2-3x.令fx=0,fy=0,可得x=0,y=0,或x=-1,y=1这2个驻点.然后求二阶偏导:fxx=6x,fxy=-3,fyy=-6y.x=0,y=0时,fxx=0,fxy=-3,fyy=0,(-3)^2-0>0,所以(0,0)不是极值点;x=-1,y=1时,fxx=-6,fxy...
求函数f(x,y)=x∧3-y∧3-3xy的极值答:f(x,y)=x^3-y^3-3xy 分别对x,y求偏导:fx=3x^2-3y fy=-3y^2-3x.令fx=0,fy=0,可得x=0,y=0,或x=-1,y=1这2个驻点.然后求二阶偏导:fxx=6x,fxy=-3,fyy=-6y.x=0,y=0时,fxx=0,fxy=-3,fyy=0,(-3)^2-0>0,所以(0,0)不是极值点;x=-1,y=1时,fxx=-6,fxy=-...
求Z=x^3-y^3-3xy的极值和极值点答:Z=f(x,y)=x^3-y^3-3xy 分别对x,y求偏导:fx=3x^2-3y fy=-3y^2-3x.令fx=0,fy=0,可得x=0,y=0,或x=-1,y=1这2个驻点.然后求二阶偏导:fxx=6x,fxy=-3,fyy=-6y.x=0,y=0时,fxx=0,fxy=-3,fyy=0,(-3)^2-0>0,所以(0,0)不是极值点;x=-1,y=1时,fxx=-6,fxy...
求Z=x^3-y^3-3xy的极值和极值点答:Z=f(x,y)=x^3-y^3-3xy分别对x,y求偏导:fx=3x^2-3yfy=-3y^2-3x.令fx=0,fy=0,可得x=0,y=0,或x=-1,y=1这2个驻点.然后求二阶偏导:fxx=6x,fxy=-3,fyy=-6y.x=0,y=0时,fxx=0,fxy=-3,fyy=0,(-3)^2-0>0,所以(0,0)不是极值点;x...
www.f-f-fxy答:在某点出一阶偏导为零,只要看黑塞矩阵的正定或负定性.对于二元函数黑塞矩阵为 A B B C 正定的充分条件是A>0且AC-B^2>0;负定的充分条件是A0;若AC-B^2>0,则矩阵不定.矩阵正定,该点为极小值;矩阵负定,该点为极大值.设A=f"xx(x,y),B=f"xy(x,y),C=f"yy(x,y),判断AC-B^...