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 \(\left( \sqrt { 2 } , - \frac { 3 } { 2 } \sqrt { 2 } \right)\)

Identify the Federal Reserve's legally mandated goals and the challenges of balancing these objectives.

Explain the concept of time inconsistency in monetary policy and its implications for economic stability.

Understand the costs of inflation and the impact of fiscal policies on the economy.

Summarize the trade-offs involved in reducing inflation and the concept of the sacrifice ratio.

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Definitions:

Risk Premium

The extra return above the risk-free rate that investors require as compensation for the risk of an investment.

Alpha

In investing, alpha is the measure of an investment's return relative to a benchmark index's performance, representing the value that a portfolio manager adds or subtracts from a fund's return.

Beta

A measure of a stock's volatility in relation to the overall market; a beta greater than 1 indicates greater volatility than the market.

Heterogeneous Expectations

A financial theory assumption that different investors have varied predictions about future market or asset performance.