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Monotonic Function

Tool to calculate the monotonicity (or not) of a function, i.e. check its direction of variation, if a function is (strictly?) monotonic (increasing or decreasing)

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Monotonic Function -

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# Monotonic Function

## Monotonic Function Tester

Tool to calculate the monotonicity (or not) of a function, i.e. check its direction of variation, if a function is (strictly?) monotonic (increasing or decreasing)

A monotonic function is a function $f$ such that for any $x_1, x_2$ if $x_1 increasing function) or$ f (x_1)> f ( x_2) $(decreasing function) but not both. In other words, a monotonic function is a function which preserves or reverses the order. ### How to determine if a function is monotone? Several methods are used to calculate the direction of variation of a function in order to know if a function is monotonic: - Calculation with its derivative: When the derivative of the function is always less than$ 0 $or always greater than$ 0 $then the function is monotonic. Example: The derivative of the function$ f(x) = x^3+1 $is$ f'(x) = 3x^2 $, the calculation of$ f'(x) >= 0 $is always verified, whatever the value of$ x $so the function$ f $is monotonic (and increasing) on$ \mathbb{R} $- Calculation with its equation: Certain functions are notoriously monotonic (either increasing or decreasing): the exponential function, etc. Example:$ x+1 $is increasing over$ \mathbb {R} \$

- Calculation with the curve of the function: a monotonic function has its curve which goes either always downwards or always upwards

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