The second derivative gives a property of the curve known as "concavity." The archetypal function to understand concavity from is a parabola. If the parabola opens upward we may show that the concavity is constant and positive. If the parabola opens downward we may show that the concavity is constant and negative.

Your function has a second derivative of

So at the critical point if is positive/negative then the point corresponds to a relative minimum/maximum.

-Dan