Find the Extreme Values of the Function Subject to the Given

question 82

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $f ( x , y ) = x y , \quad 9 x ^ { 2 } + 4 y ^ { 2 } = 36$

• A) Maximum: 3 at \(\left( \sqrt { 2 } , \frac { 3 } { 2 } \sqrt { 2 } \right) ;\) minimum: \(- 3\) at \(\left( - \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right)\)
• B) Maximum: 3 at \(\left\{ \sqrt { 2 } , \frac { 3 } { 2 } \sqrt { 2 } \right)\) and \(\left( - \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right) ;\) minimum: \(- 3\) at \(\left( \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right)\) and \(\left( - \sqrt { 2 } , \frac { 3 } { 2 } \sqrt { 2 } \right)\)
• C) Maximum: 3 at \(\left( \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right) ;\) minimum: \(- 3\) at \(\left( - \sqrt { 2 } , \frac { 3 } { 2 } \sqrt { 2 } \right)\)
• D) Maximum: 3 at \(\left\{ \sqrt { 2 } , \frac { 3 } { 2 } \sqrt { 2 } \right) ;\) minimum: \(- 3\) at \(\left( \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right)\)

---

Definitions:

Oral Agreement

An agreement made through spoken communication between parties, which can be legally binding even in the absence of a written document in some cases.

Partial Payment

A payment that covers only a portion of the total amount due on a debt, bill, or other financial obligation.

Statute of Frauds

A legal principle requiring certain types of contracts, such as those concerning real estate or lasting more than a year, to be in writing to be enforceable.

Sale of Land

The process of transferring ownership of a parcel of real estate from one party to another, typically involving a written contract and the payment of an agreed-upon price.