Search for a tool
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.

Results

Stationary Point of a Function -

Tag(s) : Functions

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Feedback and suggestions are welcome so that dCode offers the best 'Stationary Point of a Function' tool for free! Thank you!

Stationary Point of a Function

Stationary Point Calculator



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.

Source code

dCode retains ownership of the "Stationary Point of a Function" source code. Except explicit open source licence (indicated Creative Commons / free), the "Stationary Point of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Stationary Point of a Function" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Stationary Point of a Function" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Stationary Point of a Function" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Stationary Point of a Function on dCode.fr [online website], retrieved on 2024-11-21, https://www.dcode.fr/function-stationary-point

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Feedback and suggestions are welcome so that dCode offers the best 'Stationary Point of a Function' tool for free! Thank you!


https://www.dcode.fr/function-stationary-point
© 2024 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
 
Feedback