Solve the given problem by using substitution.
Find the minimum value of $f ( x , y , z ) = 2 x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } - z - 4$ subject to $z = 2 y$ .

A) $f _ { \min } = - 3.775$
B) $f _ { \min } = - 3.5$
C) $f _ { \min } = - 4$
D) $f _ { \min } = - 4.95$
E) $f _ { \min } = - 4.7$

Question

Solve the given problem by using substitution.  
Find the minimum value of $f ( x , y , z ) = 2 x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } - z - 4$ subject to $z = 2 y$ .
 
A) $f _ { \min } = - 3.775$
B) $f _ { \min } = - 3.5$
C) $f _ { \min } = - 4$
D) $f _ { \min } = - 4.95$
E) $f _ { \min } = - 4.7$

Quizplus · Accepted Answer

The Answer of Solve the given problem by using substitution.  
Find the minimum value of $f ( x , y , z ) = 2 x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } - z - 4$ subject to $z = 2 y$ .
 
A) $f _ { \min } = - 3.775$
B) $f _ { \min } = - 3.5$
C) $f _ { \min } = - 4$
D) $f _ { \min } = - 4.95$
E) $f _ { \min } = - 4.7$

Solve the Given Problem by Using Substitution f(x,y,z)=2x2+2x+y2−y+z2−z−4f ( x , y , z ) = 2 x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } - z - 4f(x,y,z)=2x2+2x+y2−y+z2−z−4

Solve the Given Problem by Using Substitution $f ( x , y , z ) = 2 x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } - z - 4$