At What Point on the Given Surface Is the Quantity $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

Multiple Choice

At what point on the given surface is the quantity $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ a minimum (The method of Lagrange multipliers can be used here.) $z = \left( 4 x ^ { 2 } + 10 x + y ^ { 2 } + 22 \right) ^ { \frac { 1 } { 2 } }$

A) $( - 1,0,5 )$
B) $( 1,0,4 )$
C) $( - 1,0,4 )$
D) $( - 1,0,6 )$
E) $( - 3,0,3 )$