Question

The minimum value of $|x|+|x+\frac{1}{2}|+|x-3|+|x-\frac{5}{2}|$ is

• A. 2
• B. 4
• C. 6

Answer 1

The correct option is C 6

$f\left(x\right)=|x|+|x+\frac{1}{2}|+|x-3|+|x-\frac{5}{2}|$
=-4x+5, for $x\le -\frac{1}{2}$
=-2x+6, for $-\frac{1}{2}\le x\le 0$
= 6, for $0\le x\le \frac{5}{2}$
=2x+1, for $\frac{5}{2}\le x\le 3$
=4x-5, for $x\ge 3$

so, minimum value of the function is 6.