Find the Maximum Value of the Function $f ( x , y ) = 6 - 4 x ^ { 2 } - y ^ { 2 }$

question 121

Multiple Choice

Find the maximum value of the function $f ( x , y ) = 6 - 4 x ^ { 2 } - y ^ { 2 }$ subject to the constraint that $4 x + y = 5$ .

• A) \(\frac { 1 } { 2 }\)
• B) \(\frac { 1 } { \sqrt { 2 } }\)
• C)1
• D) \(\sqrt { 2 }\)
• E)2
• F) \(2 \sqrt { 2 }\)
• G)4
• H) \(4 \sqrt { 2 }\)

---

Definitions:

Checks and Balances

A foundational principle in the constitution of many democratic countries, designed to ensure that no single branch of government becomes too powerful, by providing each branch with powers to check the others.

Republicanism

A political ideology centered on citizenship in a state organized as a republic under which the people hold popular sovereignty.

Liberalism

A philosophical ideology that emphasizes freedom, the approval of its citizens, and equal treatment under the law.

Social Inequality

A condition where societal resources are distributed unevenly, typically through norms of allocation that engender specific patterns along lines of socially defined categories of persons.