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I am trying to solve a problem based on some computer programming task I am trying to solve, and I have encountered a situation I am having trouble continuing..

Given a function f(x)=|1-x| + |0.5-2x| ...

How can I find it's minimum efficiently? This sum may extend to 4 or 5 more absolute values. I can try using calculus, but I found the derivative was messy, and I was not sure how to find it's zeros.

P.S. LaTeX seemed to be stuffing up, it would never update in the preview box?

Any help greatly appreciated!

Cheers,

Adrian