EXTREMUM GLOBAL ET EXTREMUM LOCAL PARTIE 1

The terms "global extremum" and "local extremum" are used in mathematics to describe the points where a function reaches its maximum (maximum) or minimum (minimum) values. Global Extremum: The global extremum of a function is the maximum (maximum) or minimum (minimum) value that the function can take over its entire domain. To find the global extremum, we examine the entire domain of the function. Local Extremum: The local extremum of a function is the maximum or minimum value that the function can take within a specific region or interval, called a neighborhood, around a particular point in the domain. To find the local extremum, we examine only a small portion of the function's domain, usually near points where the function's derivative is equal to zero. In other words, a local extremum is a point where the function appears to have a local maximum or minimum, while a global extremum is the point where the function reaches its maximum or minimum over its entire domain. To determine these points, the derivative of the function is generally used. Points where the derivative equals zero (critical points) may indicate the presence of a local extremum. However, to confirm whether it is a maximum or a minimum, the second derivative test (concavity test) can be used. In summary, global extrema are the maximum or minimum values ​​over the entire domain, while local extrema are the maximum or minimum values ​​within a specific local region.