Find the Extreme Values of the Function Subject to the Given

question 325

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = ( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$$

• A) Maximum: 81 at (-2, -4, -4); minimum: 9 at (2, 4, 4)
• B) Maximum: 49 at (-2, 4, -4); minimum: 41 at (2, -4, 4)
• C) Maximum: 77 at (-4, -4, -2); minimum: 13 at (4, 4, 2)
• D) Maximum: 77 at (-4, -2, -4); minimum: 13 at (4, 2, 4)

---

Definitions:

Universal Citizenship

The concept that all individuals, regardless of their nationality, race, or status, have the same basic rights and freedoms under international law.

Social Groups

Collections of individuals defined by shared interests, values, identities, or social connections.

Demographic Groups

Categories of populations defined by characteristics such as age, gender, ethnicity, or income.

American Work Life

The characteristics and culture surrounding employment and labor in the United States, including norms, behaviors, and expectations.