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!

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

Answers to Questions

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 online 'Stationary Point of a Function' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Stationary Point of a Function download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!