Use Lagrange Multipliers to Maximize the Function $f ( x , y ) = \sqrt { 16 - x ^ { 2 } - y ^ { 2 } }$

Multiple Choice

Use Lagrange multipliers to maximize the function $f ( x , y ) = \sqrt { 16 - x ^ { 2 } - y ^ { 2 } }$ subject to the following constraint: $x + y - 4 = 0$ Assume that x, y, and z are positive.

A) $24$
B) $\sqrt { 24 }$
C) $\sqrt { 8 }$
D) $8$
E) no absolute maximum