For each real number x, let f(x) be the minimum of the numbers 4x+1,

azizlwl

For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?

Mark44

Is this a homework problem?

azizlwl

No, Sir.
It is too taken from The Advanced Mathematical Thinking where the author said it can be solved by reversal tactic.

Sorry if it is incomplete since I copied whatever written in the book.

Bacle2

Is there a range for these numbers, i.e., is x any real number, integer, subset of these

or other?

azizlwl

2.http://physicsforums.com/showthread.php?t=632495

Bacle2

Well, the reason I was asking is that , if the minimum of these numbers is done

over different subsets of the line, then the results will be different. The solution

is straightforward: compare the functions and see which of the three dominates

over which part of the domain, and construct a piecewise function: set

f1>f2 ,f1>f3 , f2>f3 , etc., and select, for each interval the smallest.