In
calculus, the
second derivative, or the
second order 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 with respect to time. In
Leibniz notation:
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.