设z=f(x,y)在点(x 0 ,y 0 )处的某邻域内具有直到的连续偏导数,则f(x 0 ,y 0 )为函数的极大值的充分条件是( ).
A.
f x (x 0 ,y 0 )=0,f y (x 0 ,y 0 )=0
B.
[f xy (x 0 ,y 0 )] 2 -f xx (x 0 ,y 0 )f yy (x 0 ,y 0 )<0
C.
f x (x 0 ,y 0 )=0,f y (x 0 ,y 0 )=0,[f xy (x 0 ,y 0 )] 2 -f xx (x 0 ,y 0 )f yy (x 0 ,y 0 )<0,f xx (x 0 ,y 0 )>0
D.
f x (x 0 ,y 0 )=0,f y (x 0 ,y 0 )=0,[f xy (x 0 ,y 0 )] 2 -f xx (x 0 ,y 0 )f yy (x 0 ,y 0 )<0,f xx (x 0 ,y 0 )<0