Extreme value theorem
|
|
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],
- <math>f(c) \le f(x) \le f(d).<math>
The extreme value theorem is used to prove Rolle's theorem.
External link
- A Proof for extreme value theorem (http://www.cut-the-knot.org/fta/fta_note.shtml)