Solve the Problem $z = 2 - x ^ { 2 } - y ^ { 2 }$

Multiple Choice

Solve the problem.
-Find the point on the paraboloid $z = 2 - x ^ { 2 } - y ^ { 2 }$ that is closest to the point $( 1,1,2 )$ .

A) $\left( - \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)$
B) $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)$
C) $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)$
D) $\left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)$