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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Stationary Point of a Function
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Answers to Questions (FAQ)
What is a stationary point? (Definition)
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 $
How to calculate stationary points?
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).
What is a turning point?
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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