Find the Extreme Values of the Function Subject to the Given

question 117

Multiple Choice

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

• A) Maximum: 1 at (-1, -2, -3); minimum: -1 at (1, 2, 3)
• B) Maximum: 1 at (1, -2, -2); minimum: -1 at (-1, 2, 2)
• C) Maximum: 8 at (2, 1, -2); minimum: -8 at (-2, -1, 2)
• D) Maximum: 9 at (1, 2, -2); minimum: -9 at (-1, -2, 2)

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Definitions:

Drilled Oil

Petroleum that has been extracted from the earth via drilling operations, a common method for obtaining crude oil.

Inferior Goods

Goods whose demand decreases when consumer income rises, opposite to normal goods, due to their lower quality.

Demand Rises

An increase in the quantity of a good or service that consumers are willing and able to purchase at a given price.

Income Falls

A scenario where an individual or household experiences a reduction in their earnings from wages, investments, or other sources.