Find the Gradient Vector for the Scalar Function $f ( x , y ) = 10 x ^ { 2 } + 8 x y + 3 y ^ { 2 }$

question 70

Multiple Choice

Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) $f ( x , y ) = 10 x ^ { 2 } + 8 x y + 3 y ^ { 2 }$

• A) \(\nabla f ( x , y ) = ( 6 y + 8 x ) \hat { \mathbf { i } } - ( 20 x + 8 y ) \hat { \mathbf { j } }\)
• B) \(\nabla f ( x , y ) = 6 y \hat { \mathbf { i } } - 20 x \hat { \mathbf { j } }\)
• C) \(\nabla f ( x , y ) = 6 y \hat { \mathbf { i } } + 20 x \hat { \mathbf { j } }\)
• D) \(\nabla f ( x , y ) = ( 20 x + 8 y ) \hat { \mathbf { i } } + ( 6 y + 8 x ) \hat { \mathbf { j } }\)
• E) \(\nabla f ( x , y ) = 20 x \hat { \mathbf { i } } + 6 y \hat { \mathbf { j } }\)

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