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Homework Help: Is there an absolute maximum value of this function?

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the function f:R^2->R defined by f(x,y)=[e^(x+y)]-y+x. Is there an absolute maximum value of f on the set s={(x,y):/x/+/y/<=2}? Justify.

    note, /x/ is the absolute value of x.

    2. Relevant equations

    a. If f is con't, it takes compact sets to compact sets.

    b.Extreme value thm: Suppose s belongs to R^n is compact and f: s->R is continuous. then f has an absolute min value and an absolute max value on S

    3. The attempt at a solution

    My idea is
    =>show s is bounded and closed => therefore compact => f con't maps compact sets to compact sets => EVT

    but I encounted problem when finding boundary of s
    /x/+/y/<=2 that means /x/<=2 when y=0 and /y/<=2 when x=0. then can I find the boundary here by constructing a circle with x and y? cuz I saw other example did it on this way.
  2. jcsd
  3. Oct 3, 2008 #2


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