Search for a tool
Increasing Function

Tool to calculate if a function is increasing / monotonic or on which interval is increasing or strictly increasing.

Results

Increasing 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!


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

Increasing Function

Increasing Function Calculator





Answers to Questions (FAQ)

What is an increasing function?

A function $ f $ is strictly increasing if for any $$ x_1 < x_2, f(x_1) < f(x_2) $$

In other words, $ f $ has an increasing direction of variation, when $ x $ increases, $ f(x) $ also increases (not necessarily by the same quantity).

A function is said to be increasing (not strictly, in the broad sense) if for all $$ x_1 < x_2, f(x_1) \leq f(x_2) $$

Example: The function $ f(x) = x + 1 $ is increasing over its whole domain of definition $ \mathbb {R} $

The growth of a function can also be defined over an interval.

Example: The function $ f(x) = x^2 $ is strictly increasing over $ \mathbb{R}^+ $ also noted $ x > 0 $ or also $ ] 0 ; +\infty [ $

How to determine if a function is increasing?

Several methods allow to know if a function is increasing (study of the direction of variation):

- From its derivative: if the derivative of the function is greater than $ 0 $ then the function is increasing.

Example: The derivative of the function $ f(x) = x^2+2 $ is $ f'(x) = 2x $, the calculation of the inequation $ f'(x) > 0 $ is solved $ x > 0 $ so the function $ f $ is increasing when $ x > 0 $

- From its equation : Some functions are notoriously increasing, ie. the exponential function, the logarithm function, odd degree monomers, etc.

Example: $ \exp (x) $ is increasing over $ \mathbb {R} $

- From the curve of the function: an increasing function has its curve which is directed upwards.

How to determine if a linear/affine function is increasing?

A linear function of the form $ f(x) = ax + b $ is monotonic and strictly increasing over $ \mathbb{R} $ when the coefficient $ a $ is strictly positive ($ a > 0 $).

If $ a $ is negative then the function is decreasing.

If $ a = 0 $ then the function is constant.

Source code

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

Need Help ?

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

Questions / Comments

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


Source : https://www.dcode.fr/increasing-function
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback