The second derivative

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.

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

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

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