Here's one for ya.

Show that if is differentiable on an open interval , and if the graph of is concave upward on , then the graph of lies above all of its tangent lines on .

This is one of the problems given in my text. Although it is not required that I answer it, I feel that this problem could deepen my understanding of the second derivative test. Intuitively, I can visualize this, but I'm having trouble putting it into the language of math. Anybody got any Ideas?