What Point on the Surface Z Is Closest to the Origin

question 137

Multiple Choice

What point on the surface z is closest to the origin $z = x ^ { 2 } + y - 5$
Hint : Minimize the square of the distance from $( x , y , z )$ to the origin.

• A) \(( 2.5,0 , - 2.5 )\)
• B) \(\left( - 2 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)\) and \(\left( 2 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)\)
• C) \(( 0,2.5 , - 2.5 )\)
• D) \(\left( 0 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)\)
• E) \(( 0,2.5 , - 2.5 )\) and \(( 0,2.5,2.5 )\)

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