A global maximum (resp. minimum) for a real function on a set X is a value f (x₀) such that f (x) ≤ f (x₀) for all x (resp. f (x) ≥ f (x₀) for all x). The function f (x) = x³−3x on the interval [0,2] has a global minimum of −2 achieved at x = 1 which, being an interior point, is also a stationary point by Fermat’s Theorem. f(2) = 2 is a global maximum which is not a stationary point and f (0) = 0 is a local maximum which is not global and is not stationary. See also Weierstrass theorem.

The extrema of f(x)