A global maximum is the maximum value a function achieves, while the global minimum is the minimum value a function achieves. Maxima and minima can be thought of as peaks and valleys. On a bounded interval, a maximum or minimum may lie on the endpoint and may not be a peak or valley.

A function that increases without bound cannot have a global maximum. Likewise, a function that decreases without bound cannot have a minimum. Unbounded functions can have local maxima and minima.