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Maximum of a Function

Tool to determine the maximum value of a function: the maximal value that can take a function. It is a global maximum and not a local maximum.

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Maximum of a Function -

Tag(s) : Mathematics

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Maximum of a Function

Maxima Calculator

Tool to determine the maximum value of a function: the maximal value that can take a function. It is a global maximum and not a local maximum.

How to calculate a maximum?

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 maximum in $$x=m$$ over $$I$$. The value of the maximum is $$f(m)$$.

Consider $$f(x) = -x^2$$ defined over $$\mathbb{R}$$, the function reaches its maximum in $$x=0$$, $$f(x=0) = 0$$ and $$f(x) <= 0$$ over $$\mathbb{R}$$.

The maximum of a function is found when it's derivative is null and changes of sign, from positive to negative.

The maximum 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 (one speaks of a maximum of a function) or minimum (one speaks of a minimum of a function).