Tool to find the critical points of a function, corresponding to the critical values where the derivative is zero or not defined.
Critical Point of a Function - dCode
Tag(s) : Functions
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!
Critical Point of a Function
Critical Point Calculator
Answers to Questions (FAQ)
What is a critical point? (Definition)
A critical point is a point of a function where the gradient is zero or not defined (the derivative is equal to 0 or the derivative is not real). A critical point is similar to a stationary point (except for the undefined part) its value maybe maximum / minimum local / global.
How to calculate critical points?
From the function $ f $, calculate its derivative $ f '$ and look at the critical values for which it cancels $ f'(x) = $ 0 or the values for which it is not defined (see domain derivability).
Example: The square root function $ f(x) = \sqrt{x} $ has for derivative $ f'(x) = \frac{1}{2\sqrt{x}} $ which is not defined (over the reals) for $ x <= 0 $, its critical values are therefore all negative numbers (including 0).
What is the difference between a critical point and a stationary point?
A critical point is the union of all the points where the derivative is zero (called stationary points) with all the points or the derivative is not defined (called singular points).
So all stationary points are critical points but not all critical points are stationary points.
Source code
dCode retains ownership of the "Critical Point of a Function" source code. Except explicit open source licence (indicated Creative Commons / free), the "Critical Point of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Critical 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 "Critical 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 "Critical 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):
Critical Point of a Function on dCode.fr [online website], retrieved on 2024-11-21,
