Let `f(x_1,x_2,x_3,x_4)=x_1^2+x_2^2+x_3^2+x_4^2-2(x_1+x_2+x_3+x_4)+10`
and `x_1,x_3 in [-1,2]` and `x_2,x_4 in [1,4]` then the maximum value of f is

Options

A. 24
B. 20
C. 32
D. none of these

Answer

C

Explanation

`f(x_1,x_2,x_3,x_4)=(x_1-1)^2+(x_2-1)^2+(x_2-1)^2+(x_2-1)^2+(x_3-1)^2+(x_1)^2+6`
Clrearly 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`
`rArr f_("max") = 4+4+4+4+6=22`