A function’s derivative can be used to understand some behaviors of the function. Justify conclusions about the behavior of a function based on the behavior of its derivatives. The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval. The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity. The second derivative of a function may be used to locate points of inflection for the graph of the original function.