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Minimum of a Function

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.

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Minimum of a Function -

Tag(s) : Mathematics

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# Minimum of a Function

## Minima Calculator

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.

### How to calculate a 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 $$I$$. The value of the maximum is $$f(m)$$.

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

The minimum of a function is found when its derivative is null and changes of sign, from negative to positive.

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

### What is an extremum?

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