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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) : Functions

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Extremum of a Function

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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.

Answers to Questions

How to calculate a extremum?

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 \( m \) (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.

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, meaning Extremity).

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