Find the Extreme Values of the Function Subject to the Given

question 44

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = x ^ { 3 } + y ^ { 3 } + z ^ { 3 } , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$$

• A) Maximum: 8 at (2, 0, 0), (0, 2, 0), (0, 0, 2); minimum: 0 at (0, 0, 0)
• B) Maximum: 8 at (2, 0, 0); minimum: 0 at (0, 0, 0)
• C) Maximum: 8 at (2, 0, 0), (0, 2, 0), (0, 0, 2); minimum: -8 at (-2, 0, 0), (0, -2, 0), (0, 0, -2)
• D) Maximum: 8 at (2, 0, 0); minimum: -8 at (-2, 0, 0)

---

Definitions:

Legal Rights

Entitlements or permissions granted by law to individuals or entities, allowing them to perform certain actions or be treated in specific ways.

Homeland Rituals

Traditional ceremonies or practices carried out by a group of people in their native country or region.

Enslaved Africans

Individuals of African descent who were forcibly brought to and held in bondage in the Americas and other colonies, playing a central role in the transatlantic slave trade.

American-born Slaves

Individuals born into slavery in the United States, highlighting the generational aspect of slavery within the country.