The second derivative is a mathematical concept that measures how the rate of change of a function is itself changing. It is the derivative of the first derivative, providing insight into the curvature of the function's graph. If the second derivative is positive, the function is concave up, indicating that it is accelerating. Conversely, if it is negative, the function is concave down, suggesting it is decelerating. In calculus, the second derivative is often denoted as f''(x) for a function f(x). It plays a crucial role in identifying points of inflection, where the function changes its curvature, and in determining the local maxima and minima of the function.