Symmetry of second derivatives

When you look at a graph, things can be symmetric when it looks like the same things happening on either side of the middle. Symmetry of second derivatives means that when you look at the rate of change (the derivative) of something on either side of the middle, it's going in the same direction – like a mirror image. For example, if the graph is curved up on both sides, then the second derivative (the rate of change of the rate of change) is positive on both sides. This means that the graph is symmetric.