I was solving a problem on spoj, the solution of that problem requires the assumtion that,
if we add 2 the absolute value of 2 or more linear equation in x ( eg. f(x)=|5x-8| + |7x-1| + |12x-13| ) then is it necessary that f(x) (note:here f(x) denotes the sum of those terms) would montonically increasing as we go way from the optimal value of x (note: optimal value of x is the value at which x is minimum) ?
Just wanted to confirm if that statement is true or not?