How prove the maximum of 2 functions

[lmamaths]

Hi,

The maximum of 2 functions, namely f(x) and g(x) is defined as…

M(x) = ½ [ ( f + g ) + | f – g | ]

Can someone show me how this is proved out
or derived please?

Many Thx!

 

[Hurkyl]

(a) Can you prove it for numbers?
I.E. max(x, y) = ((x + y) + |x - y|) / 2

(b) Once you've done that, can you then prove it for functions?

 

[lmamaths]

How to prove the maximum of 2 functions

Thx Hurkyl,

Yes you are correct it works for both numbers as well as functions. But what I need to know is where or how did this equation come about – that is, do you know how it was created from First Principles – and please tell me how this is done if you know!

Many thx!

 

[arildno]

Well, have a look at this thread:
https://www.physicsforums.com/showthread.php?t=70702