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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.

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Extremum of a Function -

Tag(s) : Mathematics

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# Extremum of a Function

## Extremum 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 know how to find the extremum 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.

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

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

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

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

An extremum of a function is always defined over an interval (that may be the domain of definition of the function).

### What is an extrema?

Extrema is the plural form of extremum (from latin)