convex function

[Thanh Hai Dang]

Let f(x) is a convex function on [a,b]. Prove [MATH]∀c ∈(a,b)[/MATH]:
[MATH]\frac{f(c) - f(a))}{c-a}\leq \frac{f(b) - f(a))}{b-a}\leq \frac{f(b) - f(c))}{b-c} [/MATH]p/s: Sorry cause by my bad English!
Please contact me via email: thanhhai.dang2509@gmail.com.

 

[raquelc]

Note that each of those fractions is the gradient between a and c, between a and b, and c and b, where a=<c=<b.

 

[topsquark]

Please contact me via email: thanhhai.dang2509@gmail.com.

Two comments
1) Never post your personal information on a forum like this. We have no procedures or protections you can use to defend yourself from an attacker.

2) Why don't you want the response on the Forum? Others besides you might benefit and if you have further questions about it the rest of the community won't be able to help you.

-Dan

 

[Steven G]

Are there any restrictions to a, b and c.
Is it like raquelc stated that a<c<b?

 

[Steven G]

Actually I suspect it is a<c<b. Can you make a drawing of a concave up curve and check if the result is true? Then write up the proof based on the diagram.