Applied Maths. Section B2Calculus

Let f(x_1, x_2, x_3, x_4)=x_1^2+x_2^2+x_4^2-2(x_1+x_2+x_3+x_4)+10 and…

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

Answer & explanation

Correct answer: option 2

The correct answer is option (2) : 22

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

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

Also,

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

$⇒f_{max}= 4+4+4+4+6=22$