A convex function is open to the top, like this: \ / \ / \ / \/ If you connect any two points, it lies outside the curve. Which is basi

A convex function is open to the top, like this: \ / \ / \ / \/ If you connect any two points, it lies outside the curve. Which is basically the intuition for Jensen's inequality: if you go partway between two points it's above the curve, so the weighted average of the curve at those two points is bigger than the curve at their weighted average.