Find the Direction of Maximum Increase of the Function $f ( x , y , z ) = x ^ { 2 } - 2 x y + z ^ { 2 }$

question 27

Multiple Choice

Find the direction of maximum increase of the function $f ( x , y , z ) = x ^ { 2 } - 2 x y + z ^ { 2 }$ at the point $( 1,1,2 )$ .

• A) \(\{ 1,0 , - 2 \}\)
• B) \(\{ 4,1,2 \}\)
• C) \(\{ 2,1 , - 4 \}\)
• D) \(\{ 0 , - 2,4 \}\)
• E) \(\{ 2,0,3 \}\)
• F) \(\{ 3,1,2 \}\)
• G) \(\{ 0,2,1 \}\)
• H) \(( 5 , - 1,6 )\)

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