Tool to determine the minimum value of a function: the minimal value that can take a function. It is a global minimum and not a local minimum.

Minimum of a Function - dCode

Tag(s) : Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

Tool to determine the minimum value of a function: the minimal value that can take a function. It is a global minimum and not a local minimum.

For any function \( f \) defined on an interval \( I \) and \( m \) a real of this interval, if \( f(x) <= f(m) \) on the interval \( I \) then \( f \) reaches its minimum in \( x=m \) over \( I \). In that case, \( f(m) \) is the minimum value of the function, reached when \( x=m \).

The minimum of a function is always defined with an interval (which may be the domain of definition of the function).

Finding the minimum of a function \( f \), is equivalent to calculate \( f(m) \). To find \( m \), use the derivative of the function. The minimum value of a function is found when its derivative is null and changes of sign, from negative to positive.

Example: \( f(x) = x^2 \) defined over \( \mathbb{R} \), its derivative is \( f'(x) = 2x \), that is equal to zero in \( x = 0 \) because \( f'(x) = 0 \iff 2x = 0 \iff x=0 \). The derivative goes from negative to positive in \( x = 0 \) so the function has a minimum in \( x=0 \), \( f(x=0) = 0 \) and \( f(x) >= 0 \) over \( \mathbb{R} \).

An extremum is an extreme value of a function, this value can be maximum (the maximum value of the function) or minimum (the minimum value of the function).

dCode retains ownership of the source code of the script Minimum of a Function online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Minimum of a Function script for offline use on PC, iPhone or Android, ask for price quote on contact page !

minimum,function,derivative,calculation,maximum,extremum

Source : https://www.dcode.fr/minimum-function

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback