1. ## Proof

Hello

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!

2. ## 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.

3. ## Re: Proof

Originally Posted by chiro
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.

4. ## 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?

5. ## Re: Proof

Originally Posted by HallsofIvy
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!