Find the Absolute Extrema of the Function $f ( x , y ) = x ^ { 2 } + 3 y ^ { 2 } + 4 x + 10$

question 95

Short Answer

Find the absolute extrema of the function $f ( x , y ) = x ^ { 2 } + 3 y ^ { 2 } + 4 x + 10$ on the region bounded by the disk defined by $\left\{ ( x , y ) \mid x ^ { 2 } + y ^ { 2 } \leq 9 \right\}$ .

Interpret graphical representations of markets with externalities.

Understand the concept of equilibrium quantity in markets with and without externalities.

Understand the concept of technology spillovers and their implication for government policy.

Analyze the effects of public goods and positive externalities on market outcomes.

---

Definitions:

Auscultatory Gap

A temporary disappearance of sounds heard over the brachial artery when measuring blood pressure; occurs between the systolic and diastolic pressures.

Systolic Pressure

The maximum arterial pressure during contraction of the heart's left ventricle, commonly the top number in a blood pressure reading.

Diastolic Pressure

The lower measurement of blood pressure, indicating the pressure in the arteries when the heart rests between beats.

Expiration

The expulsion of air from the lungs in breathing.