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Stationary Point of a Function

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

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Stationary Point of a Function -

Tag(s) : Functions

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# Stationary Point of a Function

## Stationary Point Calculator

### 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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