# The second derivative

Source: https://projectalevel.co.uk/maths/calculus/the_second_derivative

> We offer many resources for students revising for their AS and A2 exams including: AS/A2 revision notes and practice questions, revision guides and the take a break section.

The second derivative is what you get when you differentiate the derivative.

![](https://content.projectalevel.co.uk/img/maths/second.gif)

**Stationary Points**
The second derivative can be used as an easier way of determining the nature of stationary points.

A stationary point on a curve occurs when dy/dx = 0. Once you have estabished where there is a stationary point, the type of stationary point (maximum, minimum or point of inflexion) can be determined using the second derivative.

If d²y is **positive**, then it is a **minimum point.**
 dx²

If d²y is **negative**, then it is a **maximum point.**
 dx²

If d²y is **zero**, then it could be a **max, a min or a point of inflexion.**
 dx²

If d²y/dx² = 0, you must test the values of dy/dx either side of the stationary point, as before.