Summary More Differentiation: Stationary Points There are 3 types of stationary points: maximum, minimum and point of inflexion. Differentiate once (1st differential): This tells you where there are any stationary points. Put and solve to find the value of . Use the value of to find the value of so that you have the co-ordinates of the stationary point(s). Differentiate again (2nd differential): This tells you the type of stationary point(s) you have found. Substitute your value(s) of into the 2nd differential and: If and > 0 then you have a minimum (positive is minimum). If and < 0 then you have a maximum (negative is maximum). If and = 0 then it could be maximum, minimum or point of inflexion. In the last case differentiate again: – If 0 then it is a point of inflexion. 1st differential tells us where, 2nd differential tells us type.
Summary More Differentiation: Stationary Points There are 3 types of stationary points: maximum, minimum and point of inflexion. Differentiate once (1st differential): This tells you where there are any stationary points. Put and solve to find the value of . Use the value of to find the value of so that you have the co-ordinates of the stationary point(s). Differentiate again (2nd differential): This tells you the type of stationary point(s) you have found. Substitute your value(s) of into the 2nd differential and: If and > 0 then you have a minimum (positive is minimum). If and < 0 then you have a maximum (negative is maximum). If and = 0 then it could be maximum, minimum or point of inflexion. In the last case – differentiate again: If 0 then it is a point of inflexion. 1st differential tells us where, 2nd differential tells us type.
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