Second Derivative

In calculus, the second derivative of a function f is the derivative of its derivative, informally the rate of change of the rate of change. A familiar example is the second derivative of the position of a moving object with respect to time, which is its instantaneous acceleration, the rate at which its velocity is itself changing. On the graph of a function, the sign of the second derivative corresponds to its concavity: a positive second derivative marks a graph that curves upward, while a negative one marks a graph that curves the other way.