Solve the Problem $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$

question 207

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$ at the point $( 3,4 )$ in the direction in which the function decreases most rapidly.

• A) \(- 3 \sqrt { 26 }\)
• B) \(- \sqrt { 221 }\)
• C) \(- \sqrt { 173 }\)
• D) \(- \sqrt { 167 }\)

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