Second Derivative (Leaving Cert Mathematics): Revision Notes

Second Derivative

The second derivative of a function measures how the rate of change itself is changing.

• If the first derivative tells you the slope of the graph (how fast yyy changes with xxx),
• The second derivative tells you how that slope is changing — i.e., the curvature of the graph.

The second derivative is simply the derivative of the first derivative. If $f(x)$ is a function, then the second derivative is denoted as $f''(x)$.

Example