Question

The minimum value of $f\left(x\right)=|x-1|+|x-2|+|x-3|$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

For minimum value of $f\left(x\right)$-

$f\left(x\right)\{\begin{array}{cc}-3x+6& \text{for all}x<1\\ -x+4& \text{for all}1\le x<2\\ x& \text{for all}2\le x<3\\ 3x-6& \text{for all}x\ge 3\end{array}$

From the graph it is shown that the minimum value of $f\left(x\right)$ is $2$.