Revision:The Second Derivative

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

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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 established 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 is positive, then it is a minimum point.

If is negative, then it is a maximum point.

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

If , you must test the values of either side of the stationary point, as before.

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