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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.

Answers to Questions

How to find the minimum of a function?

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 \( I \). To calculate the minimum of a function, then calculate \( f(m) \).

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).

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