Find the Gradient of the Function at the Given Point $$w = 4 x ^ { 2 } y - 3 y z + z ^ { 2 } , \quad ( 1,1 , - 2 )$$

question 36

Multiple Choice

Find the gradient of the function at the given point. $$w = 4 x ^ { 2 } y - 3 y z + z ^ { 2 } , \quad ( 1,1 , - 2 )$$

• A) \(8 \hat { \mathbf { i } } + 10 \hat { \mathbf { j } } - 5 \hat { \mathbf { k } }\)
• B) \(8 \hat { \mathbf { i } } + 10 \hat { \mathbf { j } } - 7 \hat { \mathbf { k } }\)
• C) \(4 \hat { \mathbf { i } } + 10 \hat { \mathbf { j } } - 7 \hat { \mathbf { k } }\)
• D) \(4 \hat { \mathbf { i } } + 16 \hat { \mathbf { j } } - 5 \hat { \mathbf { k } }\)
• E) \(12 \hat { \mathbf { i } } + 13 \hat { \mathbf { j } } - 7 \hat { \mathbf { k } }\)

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Definitions:

Conclusion

The statement in a logical argument that follows from the premises.

Major Premise

The first statement in a syllogism, containing the universal principle or general assertion.

Categorical Syllogism

A form of argument consisting of three categorical propositions that together yield a conclusion.

Categorical Propositions

Statements that assert or deny that all, some, or none of a particular class of objects belong to another class of objects.