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)

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Definitions:

Bilateral

Involving two parties, sides, or aspects, often referring to agreements or relationships between two entities.

Mutual Mistake

A situation in contract law where all parties involved have a mistaken belief about a vital fact upon which the contract is based.

Peerless Ship

Referencing a specific case in contract law regarding the sale of goods when there is a misunderstanding about which specific goods are being sold.

Unilateral Mistake

An error made by one party in the understanding or interpretation of facts or law related to a contract, which may not necessarily void the contract.