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:

Encoding

The process of converting information into a particular form that allows for communication or storage.

Decoding

The process by which a receiver interprets and understands a message sent by a sender.

Feedback

In the feedback loop, the sender’s interpretation of the response, which indicates whether a message was decoded and understood as intended during the communication process.

Communication Process

The series of steps through which information is transmitted from one individual or entity to another, typically involving a sender, message, medium, and receiver.