Question

What is the significance/usefulness of...

Answer 1

\[(d^2y)/dx^2\]

Answer 2

that is the notation for the second derivative, which is useful for determining whether a given stationary point of a function is a local maximum or a local minimum.

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.