As x ranges over all real values, what is the minimum value of f(x)=x−123+x−456+x−789?
Note that |x-a|+|x-b| is constant (b-a) for a<=x<=b
So, since |x-123|+|x-789| is constant for 123<=x<=789, the minimum occurs at x=456, and is 666.
So, since |x-123|+|x-789| is constant for 123<=x<=789, the minimum occurs at x=456, and is 666.