Tool to find the stationary points of a function. A stationary point is either a minimum, an extremum or a point of inflection.

Stationary Point of a Function - dCode

Tag(s) : Functions

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Definition: A stationary point (or critical point) is a point on a curve (function) where the gradient is zero (the derivative is équal to 0). A stationary point is therefore either a local maximum, a local minimum or an inflection point.

__Example:__ The curve of the order 2 polynomial $ x ^ 2 $ has a local minimum in $ x = 0 $ (which is also the global minimum)

__Example:__ $ x ^ 3 $ has an inflection point in $ x = 0 $

Calculate the derivative $ f' $ of the function $ f $ and look at the values for which it is canceled $ f'(x) = 0 $

If it changes sign from positive to negative, then it is a local maximum.

If it changes sign from negative to positive, then it is a local minimum.

If it does not change sign, then it is an inflection point.

The derivative must be differentiable at this point (check the derivability domain).

A turning point is a point on the curve where the derivative changes sign so either a local minimum or a local maximum.

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Cite as source (bibliography):

*Stationary Point of a Function* on dCode.fr [online website], retrieved on 2024-07-18,

stationary,point,inflection,maximum,minimum,function

https://www.dcode.fr/function-stationary-point

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