Provide an Appropriate Response $\mathrm { P } _ { 0 }$

question 101

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $\mathrm { P } _ { 0 }$ . $f ( x , y , z ) = x \sqrt { y ^ { 2 } + z ^ { 2 } } , P _ { 0 } ( 1,2,1 )$

• A) \(\sqrt { 30 } \left( \frac { \mathrm { i } } { 6 } + \frac { \mathrm { j } } { 15 } - \frac { \mathrm { k } } { 30 } \right)\)
• B) \(\frac { 1 } { \sqrt { 30 } } \left( \frac { i } { 6 } + \frac { j } { 15 } - \frac { k } { 30 } \right)\)
• C) \(\frac { 1 } { \sqrt { 30 } } \left( \frac { i } { 6 } + \frac { j } { 15 } + \frac { k } { 30 } \right)\)
• D) \(\sqrt { 30 } \left( \frac { \mathrm { i } } { 6 } + \frac { \mathrm { j } } { 15 } + \frac { \mathrm { k } } { 30 } \right)\)

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Definitions:

Somatogenic

A term referring to the origin of physical bodily disorders, suggesting that psychological conditions have a physical (somatic) cause.

Psychogenic

Pertains to physical illnesses or conditions that are believed to arise from emotional or mental stressors, rather than biological factors.

Abnormal Behaviour

Refers to patterns of emotion, thought, and action deemed pathological for one reason or another, often being statistically rare, violating norms, or causing distress.

Mental Hygiene Movement

An early 20th-century initiative aimed at improving mental health through prevention, early treatment, and the humane care of those with mental illness.