For $f ( x , y ) \text {, find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0 \text { and } f _ { y } ( x , y ) = 0$

question 11

Multiple Choice

For $f ( x , y ) \text {, find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0 \text { and } f _ { y } ( x , y ) = 0$ simultaneously. $f ( x , y ) = 10 x ^ { 3 } - 2 x y + 10 y ^ { 3 }$

• A) \(( 0,0 ) , \left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)\)
• B) \(\left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)\)
• C) \(\left( - \frac { 1 } { 15 } , - \frac { 1 } { 15 } \right) , \left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)\)
• D) \(\left( - \frac { 1 } { 15 } , - \frac { 1 } { 15 } \right)\)
• E) \(( 0,0 )\)

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Definitions:

Depressed

A state characterized by feelings of severe despondency and dejection, often accompanied by a lack of energy, disturbances in sleep and appetite, and loss of interest or pleasure in activities.

Friendships

A mutual relationship between two or more individuals, characterized by trust, affection, and support, regardless of blood relations.

Learned Helplessness

Learned Helplessness is a condition in which a person suffers from a sense of powerlessness, arising from a traumatic event or persistent failure to succeed.

Martin Seligman

A psychologist renowned for his work in the fields of positive psychology and learned helplessness.