Last Updated Sep 27, 2025

Second Derivative Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Second Derivative quickly and effectively.

Learn about The Basics for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of The Basics for easy recall in your Mathematics exam

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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

infoNote

Find the second derivative of $f(x)=2x^2-4x+15$

$$f'(x)=4x-4$$

$$f''(x)=4$$

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