Use Lagrange Multipliers to Solve the Problem $f ( x , y ) = 3 x y$

question 104

Multiple Choice

Use Lagrange Multipliers to solve the problem.
Find the maximum value of $f ( x , y ) = 3 x y$ subject to $x ^ { 2 } + y ^ { 2 } = 8$ .

• A) \(f _ { \max } = 24\)
• B) \(f _ { \max } = 12\)
• C) \(f _ { \max } = 17\)
• D) \(f _ { \max } = 7\)
• E) \(f _ { \max } = 32\)

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Definitions:

Serial Position Effect

A memory phenomenon where items at the beginning and end of a list are remembered better than those in the middle.

Primacy Effect

The cognitive bias that results in an individual's tendency to remember and give more weight to the first pieces of information they encounter about a topic.

Sequence Order Effect

The impact that the order of presentation has on the perception and judgment of information or stimuli.

Serial Position Effect

A memory phenomenon where recall accuracy varies as a function of an item's position within a study list, often showing enhanced memory for items at the beginning and end of the list.