The Height of a Hill (In Feet) Is Given By h

question 131

Short Answer

The height of a hill (in feet) is given by
$$h ( x , y ) = 30 \left( 14 - 5 x ^ { 2 } - 2 y ^ { 2 } + 3 x y + 30 x - 18 y \right)$$
where $x$ is the distance (in miles) east and $y$ is the distance (in miles) north of your cabin. If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

---

Definitions:

Productive Resource

An asset or input used in the production of goods and services, such as labor, land, and capital.

Trade Surplus

A Trade Surplus occurs when the value of a country's exports exceeds the value of its imports within a certain period.

Trade Deficit

A situation where a country's imports exceed its exports.

Comparative Advantage

The ability of an entity to produce a good or service at a lower opportunity cost than others, leading to specialized trade benefits.