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

question 34

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