Let f be derivative twice in (a,b) , and $\displaystyle \forall x \in (a,b) : f''(x) \geq 0 $

Prove / Give a negative example:

$\displaystyle \forall c,d \in (a,b) : f(\frac{c+d}{2}) \leq \frac{f(c)+f(d)}{2}$ .

If that's a proof, then I'll have to use a Taylor Series to explain f(x), but how do I show that one side is smaller than the other?

Thanks!