Find the Extreme Values of the Function Subject to the Given

question 52

Multiple Choice

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

• A) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left( - \frac { 6 } { 11 } , \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)
• B) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left. \} - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , \frac { 2 } { 11 } \right)\)
• C) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left\{ - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)
• D) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left\{ \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)

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Definitions:

Receptor Sites

Specific locations on the surface of a cell or within a cell that are sensitive to certain chemicals, hormones, or neurotransmitters.

Neurotransmitters

Chemicals that transmit signals across a synapse from one neuron to another in the brain and nervous system.

Dendrites

Branch-like extensions of neurons that receive signals from other neurons and are crucial for neural communication.

Serotonin

A neurotransmitter that contributes to feelings of well-being and happiness.