# Convex function

• September 21st 2010, 12:07 PM
leoemil
Convex function
Hi all, I have a simple question:

Suppose $f$ is a continously differentiable convex function on $\mathbb{R}^n$.

Then by definition (1):
$
f(t x_1 + (1-t)x_2) \leq t f(x_1) + (1-t) f(x_2)
$

$