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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Definitions:

Operant Conditioning

A learning process where the strength of a behavior is modified by reinforcement or punishment.

Observational Conditioning

A learning process where an individual acquires behaviors by observing and imitating others.

State-Dependent Learning

The theory that information learned in a specific state of mind (e.g., emotional, physiological) is more easily recalled when in that same state.

Conditioned Stimulus

An initially neutral signal that, once linked with an unconditioned stimulus, ultimately elicits a conditioned response.