Let $f\left(x_1, x_2, x_3, x_4\right)=x_1^2+x_2^2+x_3^2+x_4^2-2\left(x_1+x_2+x_3+x_4\right)+10$ and $x_1, x_3 \in[-1,2]$ and $x_2, x_4 \in[1,3]$ then the maximum value of ' $f$ ' is

22

We have,

$f\left(x_1, x_2, x_3, x_4\right)=\left(x_1-1\right)^2+\left(x_2-1\right)^2+\left(x_3-1\right)^2+\left(x_4-1\right)^2+6$

Clearly, $f$ is maximum when $x_2=x_4=3$ and $x_1=x_3=-1$

Also,

$f_{\max } =(-1-1)^2+(3-1)^2+(-1-1)^2+(3-1)^2+6$

$\Rightarrow f_{\max } =4+4+4+4+6=22$