Hi all, I have a simple question:

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

Then by definition (1):
<br /> f(t x_1 + (1-t)x_2) \leq t f(x_1) + (1-t) f(x_2)<br />

I've also read that (2):
<br /> f(x_1) \geq f(x_2) + \nabla f(x_2)[x_1-x_2]<br />

Can anybody tell me, if (1) implies (2), and why?