Provide an Appropriate Response $P _ { 0 }$ $f ( x , y ) = x y ^ { 2 } - y x ^ { 2 } , P _ { 0 } ( - 1,1 )$

question 323

Multiple Choice

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

• A) \(\left( \frac { 1 } { \sqrt { 2 } } \right) \mathrm { i } - \left( \frac { 1 } { \sqrt { 2 } } \right) j\)
• B) \(\left( \frac { 1 } { \sqrt { 2 } } \right) i + \left( \frac { 1 } { \sqrt { 2 } } \right) j\)
• C) \(\left( - \frac { 1 } { \sqrt { 2 } } \right) \mathrm { i } + \left( \frac { 1 } { \sqrt { 2 } } \right) \mathrm { j }\)
• D) \(( 1 \sqrt { 2 } ) \mathrm { i } - ( 1 \sqrt { 2 } ) \mathrm { j }\)

---

Definitions:

Divergent Thinking

A thought process or method used to generate creative ideas by exploring many possible solutions.

Emotional Intelligence

The capacity to be aware of, control, and express one's emotions, and to handle interpersonal relationships judiciously and empathetically.

Divergent Thinking

An intellectual strategy or procedure aimed at creating innovative ideas by considering a wide range of solutions.

Sternberg's Intelligences

A theory that proposes the existence of three types of intelligence: analytical, creative, and practical, as conceptualized by psychologist Robert Sternberg.