Search for a tool
Extremum of a Function

Tool to compute extrema of a function. The extremum value of a function is the minimal or maximal value that can take a function.

Results

Extremum of a Function -

Tag(s) : Functions

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 community Discord for help requests!

Thanks to your feedback and relevant comments, dCode has developed the best 'Extremum of a Function' tool, so feel free to write! Thank you!

# Extremum of a Function

## Local Minimum Calculator

Tool to compute extrema of a function. The extremum value of a function is the minimal or maximal value that can take a function.

### How to calculate a extremum?

To find the extreme values of a function (the highest or lowest points on the interval where the function is defined), first calculate the derivative of the function and make a study of sign.

An extremum of a function is reached when it's derivative is equal to zero and changes of sign.

A minimum of a function $m$ (lowercase m) exists when, for all $x$, $f(x) >= m$ is greater than or equal to a minimum $m$.

Example: The polynomial $f(x) = x^2$ defined over $\mathbb{R}$, the function has a minimum in $x=0$ and $f(x) >= 0$ over its domain of definition $\mathbb{R}$.

A maximum of a function $M$ (uppercase M) exists when for all $x$, $f(x) <= M$ is less than or equal to the maximum.

### What is the difference between a relative/local extremum and an absolute/global extremum?

An extremum of a function is necessarily defined on an interval. If the interval is the entire domain of definition of the function then it is a global/absolute extremum, otherwise it is a local/relative extremum.

### What is an extrema?

Extrema is the plural form of extremum (from latin, meaning Extremity).

## Source code

dCode retains ownership of the online 'Extremum 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 Extremum of a Function download for offline use on PC, tablet, iPhone or Android !

## Need Help ?

Please, check our community Discord for help requests!