Proof: Prove that for all w > 0, takes place f(1 + w) > f(1) + w*f(1).

[IlanSherer]

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!

 

[Deleted member 4993]

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!

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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[stapel]

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 think the above means something along the lines of the following:

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The function f(x) is increasing and convex. It begins at the point (0, 0), and is otherwise entirely within the first quadrant. Prove that, for all real numbers w > 0, the following inequality holds: f(1 + w) > f(1) + w*f(1).

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Please confirm or correct.

I have been trying for two days to solve it

When you reply, please include a clear statement of at least one of your efforts at solution. Thank you!

 

[HallsofIvy]

The fact that the function, f(x), is convex is crucial here! So what is the definition of "convex function"?