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:

Enlightenment

A philosophical movement of the 18th century, emphasizing reason, individualism, and skepticism towards traditional doctrines.

1650-1789

A historical period marked by significant developments, including the Enlightenment, the rise of modern science, and early industrialization in Europe.

1960s

A decade marked by significant social, political, and cultural changes worldwide, including civil rights movements, counterculture, and technological advancements.

Tabula Rasa

A philosophical concept suggesting that individuals are born without built-in mental content, and all knowledge comes from experience and perception.