- #1

talolard

- 125

- 0

## Homework Statement

Hey, the original question is not in english, so I am translating. So just to make sure I'm understood, i take convex to mean that the graph of the function is below the tangent.

The question:

Let F be a convex function and F is bounded from above by some number C, prove that F is static (again, my translation, by static I mean that for every x F(X)=a)

## The Attempt at a Solution

I don't think I'm close, but I am stumped, some mild hin tto point me in the right direction would be great.

we will write F as a taylor expansion:

[tex] f(x_0)+f'(x_0)(x-x_0) > f(x_0)+f'(x_0)(x-x_0) + \frac {f''(c)(x-x_0)^2}{2} <a \iff [/tex]

[tex]

0 > \frac {f''(c)(x-x_0)^2}{2} <a - f(x_0)+f'(x_0)(x-x_0) \iff [/tex]

[tex]

0 >\frac {f''(c)}{2} < \frac {a}{(x-x_0)^2} - \frac {f(x_0)+f'(x_0)}{x-x_0} [/tex]