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

**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.

Calculus

Calculus

Calculus

Calculus

Calculus

Calculus