The **second derivative** is the derivative of the derivative.

notations include:

### Physical interpretation

If f represents position, and f' velocity then f'' corresponds to acceleration(rate
of change of velocity)._{ }

Ball example

### Intuitive interpretation

f''<0 means the graph of f curves down. (think of -x^{2}.)

f''>0 means the graph curves up.(think of x^{2}.)

The **third derivative** is the derivative of the second derivative.

notice these facts