Test for Relative Extrema and Saddle Points $z = x ^ { 2 } - 8 x y + y ^ { 2 } + 120 x$

Multiple Choice

Test for relative extrema and saddle points. $z = x ^ { 2 } - 8 x y + y ^ { 2 } + 120 x$

A) saddle point at $( - 4 , - 16 , - 720 )$
B) saddle point at $( 4,16,240 )$
C) saddle point at $( 0,0,0 )$
D) relative minimum at $( 4 , - 16,1264 )$
E) relative minimum at $( 16,128,2176 )$