Find the Value of the Gradient Vector Field of the Function

question 221

Multiple Choice

Find the value of the gradient vector field of the function $f ( x , y , z ) = x ^ { 2 } y ^ { 3 } z$ at the point $( 1,1 , - 1 )$ .

• A) \(- 2 \mathbf { i } - 3 \mathbf { j } + \mathbf { k }\)
• B)\(2 \mathbf { i } + 3 \mathbf { j } + \mathbf { k }\)
• C)\(3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }\)
• D)\(3 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }\)
• E)\(6 \mathbf { i } - 6 \mathbf { j } + \mathbf { k }\)
• F)\(6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }\)
• G)\(\mathbf { i } - \mathbf { j } + \mathbf { k }\)
• H)\(\mathbf { i } + \mathbf { j } - \mathbf { k }\)

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