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Question about max of functions

  1. Sep 28, 2010 #1
    Let a,b,c,d in R. For a=< x =< b and c=< y =< d, find

    maxx{maxy{(x-a)(y-c), (x-a)(d-y), (b-x)(y-c), (b-x)(d-y)}}??

    it is well known that

    max(x,y) = [tex]\frac{x+y+|x-y|}{2}[/tex]
  2. jcsd
  3. Sep 28, 2010 #2
    With x fixed the functions you have are just straight lines... very easy to find max and min!

    maxx{maxy{(x-a)(y-c), (x-a)(d-y), (b-x)(y-c), (b-x)(d-y)}}=
    maxx{(x-a)(d-c), (x-a)(d-c), (b-x)(d-c), (b-x)(d-c)}=
    max{(b-a)(d-c), (b-a)(d-c), (b-a)(d-c), (b-a)(d-c)}=:biggrin:=(b-a)(d-c)
  4. Dec 17, 2010 #3

    but i think you didn't got what i want!

    i will try to repost my Q?

    As above we have a formula for max{x,y}. So what is the formula for max{x,y,z}?
    where x,y,z in R. In general, for x_i in R, i=1,2,..,n
    what is the formula for max{x_1, x_2,..., x_n}?

    hope anyone can got the answer!
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