Absolute Maxima and Minima
- If f(c) ≥ f(x) for all x in the domain of f, then f(c) is called the absolute maximum of f.
- If f(c) ≤ f(x) for all x in the domain of f, then f(c) is called the absolute minimum of f.
- An absolute maximum or absolute minimum is called an absolute extremum.
Extreme Value Theorem
A function f that is continuous on a closed interval [a, b] has both an absolute maximum and an absolute minimum on that interval.