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Thread: Proof

  1. #1
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    Proof

    Hello

    Help please about the following exercise :

    The function f(x) comes up and is an convex which gets out from (0,0) and continues into the first quarter.
    Prove that for all w > 0, takes place f(1 + w) > f(1) + w*f(1).

    I have been trying for two days to solve it :\

    Thanks a lot!
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  2. #2
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    Re: Proof

    Hey IlanSherer.

    Do you know the convexity constraint? You will have to use the first quarter constraint [the fact that the region is bounded by the x and y planes] and the convexity constraint to help prove this.
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  3. #3
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    Re: Proof

    Quote Originally Posted by chiro View Post
    Hey IlanSherer.

    Do you know the convexity constraint? You will have to use the first quarter constraint [the fact that the region is bounded by the x and y planes] and the convexity constraint to help prove this.
    I'm sorry, i didn't understand about "convexity constaint", what did you mean?
    We learned about definition of convex function in last lesson, and then i solved some exercises.
    But this one is hard (for me), because this exercise is more like "Put w, you will get x, and then you will get y which is a larger value than a certain value".
    Maybe i'm missing something.
    Last edited by IlanSherer; Mar 31st 2017 at 12:32 AM.
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  4. #4
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    Re: Proof

    You said that the function is "convex". Do you understand what that means? And you said "f(x) comes up"- did you mean that f(x) is convex upward? If so, first consider the line from (1, f(1)) to (1+ w, f(1+ w). If f is convex upward, what is true of that line?
    Thanks from IlanSherer
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  5. #5
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    Re: Proof

    Quote Originally Posted by HallsofIvy View Post
    You said that the function is "convex". Do you understand what that means? And you said "f(x) comes up"- did you mean that f(x) is convex upward? If so, first consider the line from (1, f(1)) to (1+ w, f(1+ w). If f is convex upward, what is true of that line?
    Yes, upward. I'm very sorry about my "Broken English".
    I got it!
    Thanks a lot!
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