extrémum
Extrémum (also extremum) is a mathematical term for a maximum or minimum value attained by a function on its domain. The input at which this value occurs is typically called a point of extremum, while the value itself is an extremum value. Extrema can be local (relative) or global (absolute). A local maximum is a point where f(x0) is at least as large as nearby values; a local minimum is at most as large as nearby values. A global maximum (absolute maximum) is the largest value of f on the entire domain, and a global minimum (absolute minimum) is the smallest.
To find local extrema of a differentiable function f, one looks at critical points where the derivative
Extrema on constrained domains require different methods, such as Lagrange multipliers. If the domain is closed
Non-smooth cases: extrema can occur at points where derivatives do not exist, for example at corners or
Applications span optimization, economics, physics, and engineering, where extrema represent optimal performance, cost, or energy.