Problem 604

[MuthuVeerappanR]

I'm not very familiar with the notion of convex/concave functions.. Especially the words 'strictly convex increasing' is confusing me..

Does the function passing through the points (1, 1), (2, 0), (3, 0) and (4, 1) satisfy the problem?? I think it's strictly convex but am not sure whether the 'increasing' mentioned the problem fits this or not?

Thanks.

EDIT: It doesn't fit. Otherwise, for the example graph in the problem, we can choose (0, 3), (1, 2), (2, 2) and (3, 3).

[Animus]

... Especially the words 'strictly convex increasing' is confusing me..

Hi Muthu,
a strictly convex increasing function is a function that is strictly convex and increasing at the same time (within the domain of definition).

An increasing function is characterized by
$f(a)<=f(b) \quad\text{ for all }\quad a<=b$.

A strictly convex function is characterized by
$\frac {f(x)-f(a)}{x-a}<\frac {f(b)-f(a)}{b-a}\quad \text{ for all }\quad a<x<b$.

Therefore you example represents a strictly convex, but not increasing function.

Cheers, Animus

[dgokman]

Can someone confirm if F(28) = ??????

[sjhillier]

Can someone confirm if F(28) = ??????

This is far too early for additional test values.