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Revision:The Second Derivative

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > The Second Derivative

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


(missing diagram)


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 \displaystyle \frac{d^2y}{dx^2} is positive, then it is a minimum point.


If \displaystyle \frac{d^2y}{dx^2} is negative, then it is a maximum point.


If \displaystyle \frac{d^2y}{dx^2} is zero, then it could be a max, a min or a point of inflexion.


If \displaystyle \frac{d^2y}{dx^2} = 0, you must test the values of \displaystyle \frac{dy}{dx}either side of the stationary point, as before.


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