Compute the Minimum Value Of $f ( x , y , z ) = x ^ { 2 } + y + z ^ { 2 }$

Essay

Compute the minimum value of $f ( x , y , z ) = x ^ { 2 } + y + z ^ { 2 }$ subject to the condition that $g ( x ) = 2 x + y + 4 z = 6$ .