Second Derivative Test

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In calculus, a branch of mathematics, the second derivative test is a criterion often useful for determining whether a given stationary point of a function is a local maximum or a local minimum using the value of the second derivative at the point. In calculus, the second derivative of a function ¿ is the derivative of the derivative of ¿. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is the instantaneous acceleration of the vehicle, or the rate at which the velocity of the vehicle is changing. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with positive second derivative curves upwards, while the graph of a function with negative second derivative curves downwards.