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Homework Help: A question about the minimum/maximum of a convex function

  1. Nov 8, 2005 #1
    I would like to be sure in the following, not prove it, just have it confirmed...
    If a function f is convex, then it has

    1.) only one maximum and no minimum
    2.) only one minimum and no maximum

    infinity and -infinity are not included.
  2. jcsd
  3. Nov 8, 2005 #2


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    It's not clear what you are asking. Since you say you want something "confirmed" it would appear you are making a statement: that either one of those two statements can be true for a convex function. That's not correct.

    A convex function is a function f, such that the set {(x,y)| y> f(x) } is convex. Given that, on (2) is true.
    (1) is true for a concave function.
  4. Nov 8, 2005 #3
    Oh, ok, I didnt make a clear distinction between a convex and a concave function.

    I didnt have a clear definition of convex and concave, so it makes more sense now, given your definition, and concave is then the opposite, and so makes (1) true.

  5. Nov 8, 2005 #4


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    In particular, y= x2 is a convex function (the set of point above its graph is convex) and y= -x2 is a concave function (the set of points above its graph is concave).
  6. Nov 13, 2005 #5
    Convex...I knew it's concave up or concave down. Well, imagine the graph of y=x^2 or y=-x^2 depending on what you're talking about. It's a simple visualisation any Algebra 2 student can do...

    bah...the guy above me wrote this exact thing.

    However, I wonder, is there such a thing as Convex?
  7. Nov 13, 2005 #6


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    yes. In terms of functions: convex = concave up & concave = concave down.

    I'm guessing that the whole up/down stuff is from a Calculus text by Stewart.
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