Question

The minimum value of $f\left(x\right)=|x-6|+|x+3|+|x-8|+|x+4|+|x-3|,x\in R$ is

Answer 1

$f\left(x\right)=|x-6|+|x+3|+|x-8|+|x+4|+|x-3|,x\in R$
Critical points are $6,-3,8,-4,3$
Minimum value occurs at median of $-4,-3,3,6,8$
Median $={\left(\frac{5+1}{2}\right)}^{th}\text{term}=3$
$\therefore$ Minimum value $=|3-6|+|3+3|+|3-8|+|3+4|+|3-3|=21$