Question

For real values of $x$ and $y$, the minimum value of $f(x,y)=x^2+2xy+2y^2+6y+10$, is

• A. 0
• B. 1
• C. 3
• D. 10

Answer 1

Answer: (B)

$f(x,y)=(x+y{)}^2+(y+3{)}^2+1$
Hence, $f(x,y)$ is minimum if $y=-3$ and $x=3$.
$\therefore f(x,y){]}_{\min }=1.$