Find the Extreme Values of the Function Subject to the Given

question 232

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = ( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 4 ) ^ { 2 } , x - y + 3 z = 7$$

• A) Maximum: none; minimum: \(\frac { 64 } { 11 }\) at \(\left( \frac { 14 } { 11 } , - \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)\)
• B) Maximum: none; minimum: \(\frac { 188 } { 11 }\) at \(\left( - \frac { 14 } { 11 } , \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)\)
• C) Maximum: none; minimum: \(\frac { 76 } { 11 }\) at \(\left( \frac { 14 } { 11 } , \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)\)
• D) Maximum: none; minimum: 36 at \(\left( \frac { 14 } { 11 } , \frac { 3 } { 11 } , - \frac { 20 } { 11 } \right)\)

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Definitions:

Functional Development

The process concerned with the growth and enhancement of the functions and capabilities of an individual, organization, or system.

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The feeling of sadness or displeasure caused by the non-fulfillment of one's hopes or expectations.