In calculus, the extreme value theorem states that if a function f(x) is continuous in the closed interval [a,b] then f(x) must attain its maximum and minimum value, each at least once.

That is, there exist numbers c, and d within the interval [a, b] such that for every value of x in [a, b],

The extreme value theorem is used to prove Rolle's theorem.

External link

• A Proof for extreme value theorem