Solve the Problem $f ( x , y , z ) = x + 2 y$

question 160

Multiple Choice

Solve the problem.
-Find the extreme values of $f ( x , y , z ) = x + 2 y$ subject to $x + y + z = 1$ and $y ^ { 2 } + z ^ { 2 } = 4$ .

• A) Maximum: \(1 + 2 \sqrt { 2 }\) at \(( 1 , \sqrt { 2 } , \sqrt { 2 } ) ;\) minimum: \(1 - 2 \sqrt { 2 }\) at \(( 1 , - \sqrt { 2 } , \sqrt { 2 } )\)
• B) Maximum: \(1 + 2 \sqrt { 2 }\) at \(( 1 , \sqrt { 2 } , - \sqrt { 2 } ) ;\) minimum: \(1 - 2 \sqrt { 2 }\) at \(( 1 , - \sqrt { 2 } , - \sqrt { 2 }\),
• C) Maximum: \(1 + 2 \sqrt { 2 }\) at \(( 1 , \sqrt { 2 } , \sqrt { 2 } )\); minimum: \(1 - 2 \sqrt { 2 }\) at \(( 1 , - \sqrt { 2 } , - \sqrt { 2 } )\)
• D) Maximum: \(1 + 2 \sqrt { 2 }\) at \(( 1 , \sqrt { 2 } , - \sqrt { 2 } ) ;\) minimum: \(1 - 2 \sqrt { 2 }\) at \(( 1 , - \sqrt { 2 } , \sqrt { 2 } )\)

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Definitions:

Free Nerve Endings

Sensory receptors located near the surface of the skin that can detect pain, temperature, and touch.

Hair Cells

Sensory cells located in the inner ear that convert sound vibrations into electrical signals that can be interpreted by the brain.

Meissner Corpuscle

Touch receptors located in the dermal papillae of the skin, sensitive to light touch and texture.

Pacinian Corpuscle

A type of mechanoreceptor found in the skin and viscera responsible for sensitivity to vibration and pressure.