Use Lagrange Multipliers to Find the Given Extremum $x$ And $y$ Are Positive

question 48

Multiple Choice

Use Lagrange multipliers to find the given extremum. In each case, assume that $x$ and $y$ are positive. Maximize $f ( x , y ) = x y$ Constraint $x + y = 10$

• A) \(f ( 7,3 ) = 21\)
• B) \(f ( 5,5 ) = 25\)
• C) \(f ( 6,4 ) = 24\)
• D) \(f ( 2,8 ) = 16\)
• E) \(f ( 1,9 ) = 9\)

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Definitions:

Secondary Radicals

are reactive intermediates in organic reactions, featuring an unpaired electron on a carbon atom that is bonded to two other carbon atoms.

Stability

The tendency of a chemical substance to maintain its chemical composition and physical state under stated conditions over time.

Energy Diagram

A graphical representation showing the energy levels of products and reactants during a chemical reaction and indicating the activation energy.

Transition State

A high-energy state during a chemical reaction where reactants are transformed into products, representing the maximum energy point along the reaction pathway.