Compute the Gradient of the Function at the Given Point $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

question 71

Multiple Choice

Compute the gradient of the function at the given point.
- $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

• A)\({\nabla} f = - i - 2 j + \frac { 10 } { 7 } \mathbf { k }\)
• B)\({\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 14 } { 5 } \mathbf { k }\)
• C)\({\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 10 } { 7 } \mathbf { k }\)
• D)\({\nabla} f = - \mathrm { i } - 2 \mathrm { j } + \frac { 14 } { 5 } \mathbf { k }\)

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Definitions:

Sociocultural Perspective

An approach in psychology that examines how social and cultural factors influence human behavior and mental processes.

Psychodynamic Perspective

A psychological approach that emphasizes unconscious psychological processes and contends that childhood experiences are crucial in shaping adult personality.

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A behaviorist is a psychologist who focuses on observable behaviors and the ways in which learning and environment influence behavior, often excluding internal processes like thoughts and emotions.

Learning Perspective

A psychological approach that emphasizes the effects of experience on behavior, suggesting that learning is the key to understanding how people think, feel, and behave.